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Abstract We revisit the nature of the ocean bottom pressure (p_b) seasonal cycle by leveraging the mounting GRACE‐basedp_brecord and its assimilation in the ocean state estimates produced by the project for Estimating the Circulation and Climate of the Ocean (ECCO). We focus on the mean seasonal cycle from both data and ECCO estimates, examining their similarities and differences and exploring the underlying causes. Despite substantial year‐to‐year variability, the 21‐year period studied (2002–2022) provides a relatively robust estimate of the mean seasonal cycle. Results indicate that thep_bannual harmonic tends to dominate but the semi‐annual harmonic can also be important (e.g., subpolar North Pacific, Bellingshausen Basin). Amplitudes and short‐scale phase variability are enhanced near coasts and continental shelves, emphasizing the importance of bottom topography in shaping the seasonal cycle inp_b. Comparisons of GRACE and ECCO estimates indicate good qualitative agreement, but considerable quantitative differences remain in many areas. The GRACE amplitudes tend to be higher than those of ECCO typically by 10%–50%, and by more than 50% in extensive regions, particularly around continental boundaries. Phase differences of more than 1 (0.5) months for the annual (semiannual) harmonics are also apparent. Larger differences near coastal regions can be related to enhanced GRACE data uncertainties and also to the absence of gravitational attraction and loading effects in ECCO. Improvements in both data and model‐based estimates are still needed to narrow present uncertainties inp_bestimates. 

We experimentally and theoretically investigate the anisotropic speed of sound of an atomic superfluid (SF) Bose-Einstein condensate in a 1D optical lattice. Because the speed of sound derives from the SF density, this implies that the SF density is itself anisotropic. We find that the speed of sound is decreased by the optical lattice, and the SF density is concomitantly reduced. This reduction is accompanied by the appearance of a zero entropy normal fluid in the purely Bose condensed phase. The reduction in SF density—first predicted [A. J. Leggett, Phys. Rev. Lett. 25, 1543 (1970).] in the context of supersolidity—results from the coexistence of superfluidity and density modulations, but is agnostic about the origin of the modulations. We additionally measure the moment of inertia of the system in a scissors mode experiment, demonstrating the existence of rotational flow. As such we shed light on some supersolid properties using imposed, rather than spontaneously formed, density order. 

The precise control of direct current (dc) magnetic fields is crucial in a wide range of experimental platforms, from ultracold quantum gases and nuclear magnetic resonance to precision measurements. In each of these cases, the Zeeman effect causes quantum states to shift in energy as a function of the magnetic field. The development of low-noise current sources is essential because electromagnets are the preferred tool to dynamically control the magnetic field. Here, we describe an ultra-low noise bipolar current source using pairs of complementary n- and p-channel metal–oxide–semiconductor field-effect transistors controlled by zero-drift operational amplifiers. Our source has a 90 kHz inherent bandwidth and provides current from −20 to 20 A with noise (0.1 Hz to 100 kHz) of 140 µA at ±20 A. 

We study gains from trade in multi-dimensional two-sided markets. Specifically, we focus on a setting with n heterogeneous items, where each item is owned by a different seller i, and there is a constrained-additive buyer with feasibility constraint ℱ. Multi-dimensional settings in one-sided markets, e.g. where a seller owns multiple heterogeneous items but also is the mechanism designer, are well-understood. In addition, single-dimensional settings in two-sided markets, e.g. where a buyer and seller each seek or own a single item, are also well-understood. Multi-dimensional two-sided markets, however, encapsulate the major challenges of both lines of work: optimizing the sale of heterogeneous items, ensuring incentive-compatibility among both sides of the market, and enforcing budget balance. We present, to the best of our knowledge, the first worst-case approximation guarantee for gains from trade in a multi-dimensional two-sided market. Our first result provides an O(log(1/r))-approximation to the first-best gains from trade for a broad class of downward-closed feasibility constraints (such as matroid, matching, knapsack, or the intersection of these). Here r is the minimum probability over all items that a buyer's value for the item exceeds the seller's cost. Our second result removes the dependence on r and provides an unconditional O(log n)-approximation to the second-best gains from trade. We extend both results for a general constrained-additive buyer, losing another O(log n)-factor en-route. The first result is achieved using a fixed posted price mechanism, and the analysis involves a novel application of the prophet inequality or a new concentration inequality. Our second result follows from a stitching lemma that allows us to upper bound the second-best gains from trade by the first-best gains from trade from the “likely to trade” items (items with trade probability at least 1/n) and the optimal profit from selling the “unlikely to trade” items. We can obtain an O(log n)-approximation to the first term by invoking our O(log(1/r))-approximation on the “likely to trade” items. We introduce a generalization of the fixed posted price mechanism—seller adjusted posted price—to obtain an O(log n)-approximation to the optimal profit for the “unlikely to trade” items. Unlike fixed posted price mechanisms, not all seller adjusted posted price mechanisms are incentive compatible and budget balanced. We develop a new argument based on “allocation coupling” to show the seller adjusted posted price mechanism used in our approximation is indeed budget balanced and incentive-compatible.