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The well-known Borde-Guth-Vilenkin Theorem shows that inflationary spacetimes are generically geodesically past-incomplete, necessitating the existence of a pre-inflationary boundary of some sort, possibly singular. I discuss the generalization of the BGV theorem to spacetimes beyond inflation, including inhomogeneous and cyclic models. As an example, I show that the cyclic model proposed by Ijjas and Steinhardt is geodesically incomplete.
Collisions between electrons and radiating atoms broaden spectral absorption and emission lines in dense plasmas. High densities also introduce screening and pressure ionization effects that distort the wavefunctions of both bound and free electrons. In order to study how dense plasma effects influence the electron broadening of spectral lines, this paper incorporates electron wavefunctions from an average-atom (AA) model to calculate the line width of the B III $2p-2s$ transition at $T = 10$ eV for mass densities ranging from $ρ=10^{-4}-0.4$ g/cc. The calculation method uses the impact approximation, allowing the line width to be written in terms of electron-collision cross sections and an interference term. Compared to an otherwise identical calculation that uses Coulomb free wavefunctions, the AA method is found to modify both the cross sections and the resulting line width at sufficiently high density by introducing screening and pressure ionized bound states. Screening lowers the cross sections at low energies and near electron excitation thresholds, while pressure ionized bound states introduce resonances into the continuum. Thus, as the density increases, the relative line w
We examine the relationship between the Null Convergence Condition (NCC) and the Borde-Guth-Vilenkin (BGV) Theorem. We first show that, for an expanding spacetime foliated orthogonally to a timelike geodesic congruence with vanishing shear and vorticity, the BGV Theorem follows when the NCC holds and the spatial curvature is non-positive, ${}^3\mathcal{R} \leq 0$. The situation becomes more complex in the presence of shear, or non-geodesic threading of the spacetime. In these cases, the local expansion that enters the BGV construction depends not only on the local scalar expansion, but acquires terms given by the contraction of the shear and acceleration with locally defined spatial unit vectors. In the general case, null convergence and non-positive curvature are no longer sufficient to guarantee that the BGV Theorem holds. We discuss the result in the context of eternal inflation in the presence of comoving curvature perturbations and state a more general version of the BGV condition relevant to asymptotically past-de Sitter eternal inflation.
An algorithm that outputs predictions about the state of the world will almost always be designed with the implicit or explicit goal of outputting accurate predictions (i.e., predictions that are likely to be true). In addition, the rise of increasingly powerful predictive algorithms brought about by the recent revolution in artificial intelligence has led to an emphasis on building predictive algorithms that are fair, in the sense that their predictions do not systematically evince bias or bring about harm to certain individuals or groups. This state of affairs presents two conceptual challenges. First, the goals of accuracy and fairness can sometimes be in tension, and there are no obvious normative guidelines for managing the trade-offs between these two desiderata when they arise. Second, there are many distinct ways of measuring both the accuracy and fairness of a predictive algorithm; here too, there are no obvious guidelines on how to aggregate our preferences for predictive algorithms that satisfy disparate measures of fairness and accuracy to various extents. The goal of this paper is to address these challenges by arguing that there are good reasons for using a linear com
This work extends the previously developed mean force emission theory to describe electron-ion plasmas. Results are compared to molecular dynamics simulations. The main extensions are to account for the attractive nature of electron-ion interactions and to model short-range quantum effects using the Kelbg potential. By reducing the electron-ion force inside the deBroglie wavelength, the Kelbg potential causes a decay at high frequencies and a decrease in magnitude of the low frequency bremsstrahlung spectrum. The attractive electron-ion interaction also allows for classically bound states that show up as peaks in the emission spectrum. Results show that the Kelbg potential can capture quantum modifications to classical Gaunt factors, but is limited in describing emission at very high frequencies. This work further supports the notion that there is a peak in emission near the plasma frequency at strong coupling that cannot be captured using the common Drude correction. Importantly, the linear response framework used to calculate the bremsstrahlung emission coefficient is related to both the absorption coefficient and the real part of the dynamic electrical conductivity. This means t
We present a method to convert weather data into probabilistic forecasts of Aedes aegypti abundance. The approach, which relies on the Aedes-AI suite of neural networks, produces weekly point predictions with corresponding uncertainty estimates. Once calibrated on past trap and weather data, the model is designed to use weather forecasts to estimate future trap catches. We demonstrate that when reliable input data are used, the resulting predictions have high skill. This technique may therefore be used to supplement vector surveillance efforts or identify periods of elevated risk for vector-borne disease outbreaks.
Deep learning is a powerful set of techniques for detecting complex patterns in data. However, when the causal structure of that process is underspecified, deep learning models can be brittle, lacking robustness to shifts in the distribution of the data-generating process. In this paper, we turn to loop polarity analysis as a tool for specifying the causal structure of a data-generating process, in order to encode a more robust understanding of the relationship between system structure and system behavior within the deep learning pipeline. We use simulated epidemic data based on an SIR model to demonstrate how measuring the polarity of the different feedback loops that compose a system can lead to more robust inferences on the part of neural networks, improving the out-of-distribution performance of a deep learning model and infusing a system-dynamics-inspired approach into the machine learning development pipeline.
We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves {stochastic mathematical systems} (SMSs), which are stochastic processes that generate pairs of questions and associated answers (with no explicit referents). We use the SMS framework to define normative conditions for mathematical reasoning, by defining a ``calibration'' relation between a pair of SMSs. The first SMS is the human reasoner, and the second is an ``oracle'' SMS that can be interpreted as deciding whether the question-answer pairs of the reasoner SMS are valid. To ground thinking, we understand the answers to questions given by this oracle to be the answers that would be given by an SMS representing the entire mathematical community in the infinite long run of the process of asking and answering questions. We then introduce a slight extension of SMSs to allow us to model both the physical universe and human reasoning about the physical universe. We then define a slightly different calibration relation appropriate for the case of scientific reasoning. In this case the first SMS represents a human scientist predicting the outcome of future e
We present a Hubble Space Telescope (HST) survey of extended [OIII] emission for a sample of 60 Seyfert galaxies (22 Seyfert 1's and 38 Seyfert 2's), selected based on their far infrared properties. The observations for 42 of these galaxies were done in a snapshot survey with WFPC2. The remaining 18 were obtained from the HST archive, most of which were observed with the same configuration. These observations cover 68% of the objects in the sample defined by Kinney et al. (2000), and create a valuable dataset for the study of the Narrow Line Region (NLR) properties of Seyfert galaxies. In this paper, we present the details of the observations, reductions, and measurements. We also discuss the extended structure of individual sources, and the relation of this emission to the radio and host galaxy morphology. We also address how representative the subsample of [O III]-imaged galaxies is of the entire sample, and possible selection effects that may affect this comparison of the properties of Seyfert 1 and Seyfert 2 galaxies.
We construct a family of simple single-field inflation models consistent with Planck / BICEP Keck bounds which have a parametrically small tensor amplitude and no running of the scalar spectral index. The construction consists of a constant-roll hilltop inflaton potential with the end of inflation left as a free parameter induced by higher-order operators which become dominant late in inflation. This construction directly demonstrates that there is no lower bound on the tensor/scalar ratio for simple single-field inflation models.
A supermassive black hole has been found lurking about 30,000 light-years from the center of its galaxy—the first dormant black hole detected so far from a galactic core。 It revealed itself only after shredding a passing star and producing a brief, brilliant flare。 Astronomers think it may be the remnant of a devoured galaxy or a black hole flung o
Scientists have demonstrated that heat can move through a crystal in focused, wave-like rays at room temperature instead of spreading randomly。 The breakthrough could make it possible to route heat around sensitive parts of next-generation chips and quantum devices
Scientists have generated quantum entanglement directly from sunlight, potentially offering a lower-energy alternative to the lasers normally used in quantum technology。 Their outdoor experiment produced entangled photons with about 94% similarity to an ideal state。 The result could pave the way for simpler quantum satellites, secure communications
Scientists have successfully generated electricity with a hydrogen turbine that produces its own pressure through detonation waves instead of relying on a mechanical compressor。 The breakthrough could unlock dramatically more efficient power systems for clean energy and future aviation
A mathematician working at Anthropic says he used the AI model Claude Fable 5 to uncover a remarkably simple counterexample to the Jacobian conjecture, a famous problem that has resisted mathematicians for more than a century。 The result shows that the conjecture is false in three dimensions and above, although the original two-dimensional version
A ten-month Antarctic experiment found that astronauts may struggle not only with loneliness but also with spending too much time around the same people。 Frequent contact was linked to greater tension and mistrust, while the crew increasingly divided into cultural and language-based groups