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With its extreme axial tilt, Uranus' radiant energy budget (REB) and internal heat flux remain among the most intriguing mysteries in our solar system. By combining observations with modeling, we present the global REB over a complete orbital period (1946–2030), revealing significant seasonal variations. Despite these fluctuations, the global average emitted thermal power consistently exceeds absorbed solar power, indicating a net energy loss. Assuming no significant seasonal variation in emitted power, we estimate an internal heat flux of 0.078 ± 0.018 W/m2 by analyzing the energy budget over one orbital period. The combination of internal heat and radiant energies indicates substantial global and hemispheric imbalances, with excesses or deficits exceeding 85% of emitted power at the hemispheric scale. These findings are crucial for understanding Uranus' interior and atmosphere. A future flagship mission to Uranus would provide critical observations to address more unresolved questions of this enigmatic ice giant. 

Abstract The global energy budget is pivotal to understanding planetary evolution and climate behaviors. Assessing the energy budget of giant planets, particularly those with large seasonal cycles, however, remains a challenge without long-term observations. Evolution models of Saturn cannot explain its estimated Bond albedo and internal heat flux, mainly because previous estimates were based on limited observations. Here, we analyze the long-term observations recorded by the Cassini spacecraft and find notably higher Bond albedo (0.41 ± 0.02) and internal heat flux (2.84 ± 0.20 Wm⁻²) values than previous estimates. Furthermore, Saturn’s global energy budget is not in a steady state and exhibits significant dynamical imbalances. The global radiant energy deficit at the top of the atmosphere, indicative of the planetary cooling of Saturn, reveals remarkable seasonal fluctuations with a magnitude of 16.0 ± 4.2%. Further analysis of the energy budget of the upper atmosphere including the internal heat suggests seasonal energy imbalances at both global and hemispheric scales, contributing to the development of giant convective storms on Saturn. Similar seasonal variabilities of planetary cooling and energy imbalance exist in other giant planets within and beyond the Solar System, a prospect currently overlooked in existing evolutional and atmospheric models. 

Differential privacy (DP) is a widely used notion for reasoning about privacy when publishing aggregate data. In this paper, we observe that certain DP mechanisms are amenable to a posteriori privacy analysis that exploits the fact that some outputs leak less information about the input database than others. To exploit this phenomenon, we introduce output differential privacy (ODP) and a new composition experiment, and leverage these new constructs to obtain significant privacy budget savings and improved privacy–utility tradeoffs under composition. All of this comes at no cost in terms of privacy; we do not weaken the privacy guarantee. To demonstrate the applicability of our a posteriori privacy analysis techniques, we analyze two well-known mechanisms: the Sparse Vector Technique and the Propose-Test-Release framework. We then show how our techniques can be used to save privacy budget in more general contexts: when a differentially private iterative mechanism terminates before its maximal number of iterations is reached, and when the output of a DP mechanism provides unsatisfactory utility. Examples of the former include iterative optimization algorithms, whereas examples of the latter include training a machine learning model with a large generalization error. Our techniques can be applied beyond the current paper to refine the analysis of existing DP mechanisms or guide the design of future mechanisms. 

Computational models of distributional semantics can analyze a corpus to derive representations of word meanings in terms of each word’s relationship to all other words in the corpus. While these models are sensitive to topic (e.g., tiger and stripes) and synonymy (e.g., soar and fly), the models have limited sensitivity to part of speech (e.g., book and shirt are both nouns). By augmenting a holographic model of semantic memory with additional levels of representations, we present evidence that sensitivity to syntax is supported by exploiting associations between words at varying degrees of separation. We find that sensitivity to associations at three degrees of separation reinforces the relationships between words that share part-of-speech and improves the ability of the model to construct grammatical sentences. Our model provides evidence that semantics and syntax exist on a continuum and emerge from a unitary cognitive system.