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In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is approximating cuts in balanced directed graphs, where the goal is to build a data structure to provide a $(1 \pm \epsilon)$-estimation of the cut values of a graph on $n$ vertices. For this problem, there are tight bounds for undirected graphs, but for directed graphs, such a data structure requires $\Omega(n^2)$ bits even for constant $\epsilon$. To cope with this, recent works consider $\beta$-balanced graphs, meaning that for every directed cut, the total weight of edges in one direction is at most $\beta$ times the total weight in the other direction. We consider the for-each model, where the goal is to approximate a fixed cut with high probability, and the for-all model, where the data structure must simultaneously preserve all cuts. We improve the previous $\Omega(n \sqrt{\beta/\epsilon})$ lower bound in the for-each model to $\tilde\Omega(n \sqrt{\beta}/\epsilon)$ and we improve the previous $\Omega(n \beta/\epsilon)$ lower bound in the for-all model to $\Omega(n \beta/\epsilon^2)$. This resolves the main open questions of (Cen et al., ICALP, 2021). The second problem is approximating the global minimum cut in the local query model where we can only access the graph through degree, edge, and adjacency queries. We prove an $\Omega(\min\{m, \frac{m}{\epsilon^2 k}\})$ lower bound for this problem, which improves the previous $\Omega(\frac{m}{k})$ lower bound, where $m$ is the number of edges of the graph, $k$ is the minimum cut size, and we seek a $(1+\epsilon)$-approximation. In addition, we observe that existing upper bounds with minor modifications match our lower bound up to logarithmic factors. 

The libration spectrum of liquid H2O is resolved into an octupolar twisting libration band at 485 cm−1 and dipolar rocking–wagging libration bands at 707 and 743 cm−1 using polarization analysis of the hyper-Raman scattering (HRS) spectrum. Dipole interactions and orientation correlation over distances less than 2 nm account for the 36 cm−1 splitting of the longitudinal and transverse polarized bands of the dipolar rocking–wagging libration mode, while the intensity difference observed for the bands is the result of libration correlation over distances larger than 200 nm. The coupled rock and wag libration in water is similar to libration modes in ice. The libration relaxation time determined from the width of the spectrum is 36–54 fs. Polarization analysis of the HRS spectrum also shows long range correlation for molecular orientation and hindered translation, bending and stretching vibrations in water. 

Abstract. This paper provides an overview and demonstration of emerging float-based methods for quantifying gross primary production (GPP) and net community production (NCP) using Biogeochemical-Argo (BGC-Argo) float data. Recent publications have described GPP methods that are based on the detection of diurnal oscillations in upper-ocean oxygen or particulate organic carbon concentrations using single profilers or a composite of BGC-Argo floats. NCP methods rely on budget calculations to partition observed tracer variations into physical or biological processes occurring over timescales greater than 1 d. Presently, multi-year NCP time series are feasible at near-weekly resolution, using consecutive or simultaneous float deployments at local scales. Results, however, are sensitive to the choice of tracer used in the budget calculations and uncertainties in the budget parameterizations employed across different NCP approaches. Decadal, basin-wide GPP calculations are currently achievable using data compiled from the entire BGC-Argo array, but finer spatial and temporal resolution requires more float deployments to construct diurnal tracer curves. A projected, global BGC-Argo array of 1000 floats should be sufficient to attain annual GPP estimates at 10∘ latitudinal resolution if floats profile at off-integer intervals (e.g., 5.2 or 10.2 d). Addressing the current limitations of float-based methods should enable enhanced spatial and temporal coverage of marine GPP and NCP measurements, facilitating global-scale determinations of the carbon export potential, training of satellite primary production algorithms, and evaluations of biogeochemical numerical models. This paper aims to facilitate broader uptake of float GPP and NCP methods, as singular or combined tools, by the oceanographic community and to promote their continued development.

 

Collective modes and dynamics of dense disordered materials such as water are not well understood, but nonlinear optics provides a sensitive probe to study polar modes in these materials. Here we report the hyper- Raman (HRS) light scattering spectrum measured for liquid D2O decomposed into contributions from transverse and longitudinal dipolar modes and octupolar modes, using the polarization dependence of HRS. Transverse HRS is observed for orientation and stretching modes, while longitudinal HRS is observed for translation, libration, and bending modes. The HRS observations indicate molecular correlation at distances >200 nm for all modes of orientation, libration, and vibration. The rocking/wagging, twisting, and translation modes for D2O molecules in the hydrogen bonded network are distinguished. The LO-TO splitting is 28 cm−1 for the libration mode and 16 cm−1 for the translation mode, and the relaxation time for libration modes is about 80 fs. The long-range correlation of the orientation and stretching modes is explained as the result of the dipole-dipole orientation correlation in a dipolar fluid. The long-range correlation of the longitudinal polarized libration and bending modes needs further study. 

We report on a full-polarization analysis of the first 25 as yet nonrepeating fast radio bursts (FRBs) detected at 1.4 GHz by the 110-antenna Deep Synoptic Array (DSA-110) during commissioning observations. We present details of the data-reduction, calibration, and analysis procedures developed for this novel instrument. Faraday rotation measures (RMs) are searched between ±10⁶rad m⁻²and detected for 20 FRBs, with magnitudes ranging from 4 to 4670 rad m⁻². Fifteen out of 25 FRBs are consistent with 100% polarization, 10 of which have high (≥70%) linear-polarization fractions and two of which have high (≥30%) circular-polarization fractions. Our results disfavor multipath RM scattering as a dominant depolarization mechanism. Polarization-state and possible RM variations are observed in the four FRBs with multiple subcomponents. We combine the DSA-110 sample with polarimetry of previously published FRBs, and compare the polarization properties of FRB subpopulations and FRBs with Galactic pulsars. Although FRB polarization fractions are typically higher than those of Galactic pulsars, and cover a wider range than those of pulsar single pulses, they resemble those of the youngest (characteristic ages <10⁵yr) pulsars. Our results support a scenario wherein FRB emission is intrinsically highly linearly polarized, and propagation effects can result in conversion to circular polarization and depolarization. Young pulsar emission and magnetospheric propagation geometries may form a useful analogy for the origin of FRB polarization.