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Minimization Fractional Prophet Inequalities for Sequential Procurement
No full textWe consider a minimization variant on the classical prophet inequality with monomial cost functions. A firm would like to procure some fixed amount of a divisible commodity from sellers that arrive sequentially. Whenever a seller arrives, the seller’s cost function is revealed, and the firm chooses how much of the commodity to buy. We first show that if one restricts the set of distributions for the coefficients to a family of natural distributions that include, for example, the uniform and truncated normal distributions, then there is a thresholding policy that is asymptotically optimal in the number of sellers. We then compare two scenarios based on whether the firm has in-house production capabilities or not. We precisely compute the optimal algorithm’s competitive ratio when in-house production capabilities exist and for a special case when they do not. We show that the main advantage of the ability to produce the commodity in house is that it shields the firm from price spikes in worst-case scenarios
Pelagic calcium carbonate production and shallow dissolution in the North Pacific Ocean
No full textPlanktonic calcifying organisms play a key role in regulating ocean carbonate chemistry and atmospheric CO₂. Surprisingly, references to the absolute and relative contribution of these organisms to calcium carbonate production are lacking. Here we report quantification of pelagic calcium carbonate production in the North Pacific, providing new insights on the contribution of the three main planktonic calcifying groups. Our results show that coccolithophores dominate the living calcium carbonate (CaCO₃) standing stock, with coccolithophore calcite comprising ~90% of total CaCO₃ production, and pteropods and foraminifera playing a secondary role. We show that pelagic CaCO₃ production is higher than the sinking flux of CaCO₃ at 150 and 200 m at ocean stations ALOHA and PAPA, implying that a large portion of pelagic calcium carbonate is remineralised within the photic zone; this extensive shallow dissolution explains the apparent discrepancy between previous estimates of CaCO₃ production derived from satellite observations/biogeochemical modeling versus estimates from shallow sediment traps. We suggest future changes in the CaCO₃ cycle and its impact on atmospheric CO₂ will largely depend on how the poorly-understood processes that determine whether CaCO₃ is remineralised in the photic zone or exported to depth respond to anthropogenic warming and acidification
Hierarchical Porous Monoliths of Steel with Self-Reinforcing Adaptive Properties
No full textPorous structures offer an attractive approach to reduce the amount of natural resources used while maintaining relatively high mechanical efficiency. However, for some applications the drop in mechanical properties resulting from the introduction of porosity is too high, which has limited the broader utilization of porous materials in industry. Here, it is shown that steel monoliths can be designed to display high mechanical efficiency and reversible self-reinforcing properties when made with porous architectures with up to three hierarchical levels. Ultralight steel structures that can float on water and autonomously adapt their stiffness are manufactured by the thermal reduction and sintering of 3D printed foam templates. Using distinct mechanical testing techniques, image analysis, and finite element simulations, the mechanisms leading to the high mechanical efficiency and self-stiffening ability of the hierarchical porous monoliths are studied. The design and fabrication of mechanically stable porous monoliths using iron as a widely available natural resource is expected to contribute to the future development of functional materials with a more sustainable footprint
Origin of the superchondritic carbon/nitrogen ratio of the bulk silicate Earth – an outlook from iron meteorites
No full textDisagreement regarding the origin of the bulk silicate Earth’s (BSE) superchondritic carbon/nitrogen (C/N) ratio is due, in part, to the unknown C/N ratios of differentiated planetesimals – the building blocks of Earth-like rocky planets. In this study we report solid–liquid metal partitioning experiments for C and N that allow us to reconstruct, from the C and N contents of iron meteorites, the C/N ratios of the cores of the earliest formed planetesimals. Due to their siderophile character, most of the C and N retained in these bodies after differentiation resides in their cores. Therefore, estimates of the bulk C and N contents and C/N ratios of the cores yield confident estimates of these quantities in the complete parent bodies of iron meteorites. Our experimental data, at 1 GPa and 1200–1400 °C, show that C and N are incompatible in solid metal relative to S-poor liquids but compatible in solid metal relative to S-rich liquids. Crucially, N is approximately an order of magnitude more compatible than C in S-rich systems. S itself is incompatible in solid metal and so the late-crystallizing liquids persisting at the end of core freezing were S-rich for most cores. Although these late-crystallizing liquids are unsampled by iron meteorites, we infer that their N contents and C/N ratios were generally lower and higher, respectively, than those in iron meteorites. Depending upon the fraction of unsampled late-crystallizing liquids as well as their S contents, the C/N ratios of the bulk cores and complete parent bodies are either similar to or higher than those measured in iron meteorites. The reconstructed C/N ratios of most of the parent bodies of iron meteorites are chondritic, except that the volatile-rich IC and IIC groups have superchondritic C/N ratios. Importantly, the C/N ratio of the parent body of the IC iron meteorite group lies within the estimated range of the BSE, whereas the C/N ratios of all other groups are lower. Correlated depletion of moderately volatile elements like Ge and Ga with C and N, variations in metallographic cooling rates, and Pd-Ag isotope systematics suggest that the parent cores of the volatile-depleted iron meteorite groups were likely affected by volatile degassing. If volatile-rich iron meteorite groups like the IC better capture the C and N inventories of the parent cores of the earliest formed planetesimals, then delivery of C and N via such planetesimals makes the superchondritic C/N ratio of the BSE a natural consequence of the Earth’s accretion history. Otherwise, poorly constrained processes like atmospheric erosion or C and N delivery by exotic materials are required to explain the superchondritic C/N ratio of the BSE
TOI-561 b: A Low-density Ultra-short-period “Rocky” Planet around a Metal-poor Star
No full textTOI-561 is a galactic thick-disk star hosting an ultra-short-period (0.45-day-orbit) planet with a radius of 1.37 R_⊕, making it one of the most metal-poor ([Fe/H] = −0.41) and oldest (≈10 Gyr) sites where an Earth-sized planet has been found. We present new simultaneous radial velocity (RV) measurements from Gemini-N/MAROON-X and Keck/HIRES, which we combined with literature RVs to derive a mass of M_ = 2.24 ± 0.20 M_⊕. We also used two new sectors of TESS photometry to improve the radius determination, finding R_b = 1.37 ± 0.04 R_⊕ and confirming that TOI-561 b is one of the lowest-density super-Earths measured to date (ρ_b = 4.8 ± 0.5 g cm⁻³). This density is consistent with an iron-poor rocky composition reflective of the host star’s iron and rock-building element abundances; however, it is also consistent with a low-density planet with a volatile envelope. The equilibrium temperature of the planet (∼2300 K) suggests that this envelope would likely be composed of high mean molecular weight species, such as water vapor, carbon dioxide, or silicate vapor, and is likely not primordial. We also demonstrate that the composition determination is sensitive to the choice of stellar parameters and that further measurements are needed to determine whether TOI-561 b is a bare rocky planet, a rocky planet with an optically thin atmosphere, or a rare example of a nonprimordial envelope on a planet with a radius smaller than 1.5 R_⊕
Score-based Diffusion Models in Function Space
No full textDiffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising. Despite their tremendous success, they are mostly formulated on finite-dimensional spaces, e.g. Euclidean, limiting their applications to many domains where the data has a functional form such as in scientific computing and 3D geometric data analysis. In this work, we introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. In DDOs, the forward process perturbs input functions gradually using a Gaussian process. The generative process is formulated by integrating a function-valued Langevin dynamic. Our approach requires an appropriate notion of the score for the perturbed data distribution, which we obtain by generalizing denoising score matching to function spaces that can be infinite-dimensional. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost that is independent of the data resolution. We theoretically and numerically verify the applicability of our approach on a set of problems, including generating solutions to the Navier-Stokes equation viewed as the push-forward distribution of forcings from a Gaussian Random Field (GRF)
Vision Transformers Are Good Mask Auto-Labelers
No full textWe propose Mask Auto-Labeler (MAL), a high-quality Transformer-based mask auto-labeling framework for instance segmentation using only box annotations. MAL takes box-cropped images as inputs and conditionally generates their mask pseudo-labels.We show that Vision Transformers are good mask auto-labelers. Our method significantly reduces the gap between auto-labeling and human annotation regarding mask quality. Instance segmentation models trained using the MAL-generated masks can nearly match the performance of their fully-supervised counterparts, retaining up to 97.4% performance of fully supervised models. The best model achieves 44.1% mAP on COCO instance segmentation (test-dev 2017), outperforming state-of-the-art box-supervised methods by significant margins. Qualitative results indicate that masks produced by MAL are, in some cases, even better than human annotations
A Finite-Sample Analysis of Payoff-Based Independent Learning in Zero-Sum Stochastic Games
No full textWe study two-player zero-sum stochastic games, and propose a form of independent learning dynamics called Doubly Smoothed Best-Response dynamics, which integrates a discrete and doubly smoothed variant of the best-response dynamics into temporal-difference (TD)-learning and minimax value iteration. The resulting dynamics are payoff-based, convergent, rational, and symmetric among players. Our main results provide finite-sample guarantees. In particular, we prove the first-known O̅(1/ϵ²) sample complexity bound for payoff-based independent learning dynamics, up to a smoothing bias. In the special case where the stochastic game has only one state (i.e., matrix games), we provide a sharper O̅(1/ϵ) sample complexity. Our analysis uses a novel coupled Lyapunov drift approach to capture the evolution of multiple sets of coupled and stochastic iterates, which might be of independent interest
Single-shot 3D photoacoustic tomography using a single-element detector for ultrafast imaging of hemodynamics
No full textImaging hemodynamics is crucial for the diagnosis, treatment, and prevention of vascular diseases. However, current imaging techniques are limited due to the use of ionizing radiation or contrast agents, short penetration depth, or complex and expensive data acquisition systems. Photoacoustic tomography shows promise as a solution to these issues. However, existing photoacoustic tomography methods collect signals either sequentially or through numerous detector elements, leading to either low imaging speed or high system complexity and cost. To address these issues, here we introduce a method to capture a 3D photoacoustic image of vasculature using a single laser pulse and a single-element detector that functions as 6,400 virtual ones. Our method enables ultrafast volumetric imaging of hemodynamics in the human body at up to 1 kHz and requires only a single calibration for different objects and for long-term operations. We demonstrate 3D imaging of hemodynamics at depth in humans and small animals, capturing the variability in blood flow speeds. This concept can inspire other imaging technologies and find applications such as home-care monitoring, biometrics, point-of-care testing, and wearable monitoring
Staphylococcal secreted cytotoxins are competition sensing signals for Pseudomonas aeruginosa
No full textCoinfection with two notorious opportunistic pathogens, the Gram-negative Pseudomonas aeruginosa and Gram-positiveStaphylococcus aureus, dominates chronic pulmonary infections. While coinfection is associated with poor patient outcomes, the interspecies interactions responsible for such decline remain unknown. Here, we dissected molecular mechanisms of interspecies sensing between P. aeruginosa and S. aureus. We discovered that P. aeruginosa senses S. aureus secreted peptides and, counterintuitively, moves towards these toxins. P. aeruginosa tolerates such a strategy through “competition sensing”, whereby it preempts imminent danger/competition by arming cells with type six secretion (T6S) and iron acquisition systems. Intriguingly, while T6S is predominantly described as weaponry targeting Gram-negative and eukaryotic cells, we find that T6S is essential for full P. aeruginosa competition with S. aureus, a previously undescribed role for T6S. Importantly, competition sensing was activated during coinfection of bronchial epithelia, including T6S islands targeting human cells. This study reveals critical insight into both interspecies competition and how antagonism may cause collateral damage to the host environment