Higher uniformity of bounded multiplicative functions in short intervals on average

Let λ denote the Liouville function. We show that, as X → ∞, ∫^(2X)_X sup_(P(Y)∈R[Y]degP≤k) ∣∣∣ ∑_(x≤n≤x+H) λ(n)e(−P(n))∣∣∣∣ dx = o(XH) for all fixed k and X^θ ≤ H ≤ X with 0 < θ < 1 fixed but arbitrarily small. Previously this was only established for k ≤ 1. We obtain this result as a special case of the corresponding statement for (non-pretentious) 1-bounded multiplicative functions that we prove. In fact, we are able to replace the polynomial phases e(−P(n)) by degree k nilsequences F̅(g(n)Γ). By the inverse theory for the Gowers norms this implies the higher order asymptotic uniformity result ∫^(2X)_X ∥λ∥_(U^(k+1))([x,x+H]) dx = o(X)in the same range of H. We present applications of this result to patterns of various types in the Liouville sequence. Firstly, we show that the number of sign patterns of the Liouville function is superpolynomial, making progress on a conjecture of Sarnak about the Liouville sequence having positive entropy. Secondly, we obtain cancellation in averages of λ over short polynomial progressions (n+P₁(m),…,n+Pₖ(m)), which in the case of linear polynomials yields a new averaged version of Chowla's conjecture. We are in fact able to prove our results on polynomial phases in the wider range H ≥ exp((log X)^(5/(8+ε))), thus strengthening also previous work on the Fourier uniformity of the Liouville function

Transgenerational exposure to deoxygenation and warming disrupts mate-detection in Gammarus locusta

Ocean deoxygenation and warming have been shown to pose a growing threat to the health of marine organisms and ecosystems. Yet, the potential for acclimation and adaptation to these threats remains poorly understood. The aim of this study was to evaluate the effects of transgenerational exposure to reduced oxygen availability and elevated seawater temperature on the chemosensory-dependent mating mechanisms of male amphipodsGammarus locusta. After exposure, the number of individuals that reached adulthood (in F0 and F2) was gauged, and adult males from F0 and F1 were subjected to behavioral trials to assess their capacity of long-distance female cue detection through quantification of (i) response time; (ii) first direction of movement; (iii) activity rate and (iv) proportion of time spent in female scent cues. Ocean warming induced mortality (especially in F2), and reduced oxygen availability had adverse effects on each of the investigated behavioral traits, which were amplified when combined with elevated temperature. Still, when compared to F0, the F1 generation demonstrated more adaptability (i.e., higher activity rate and preference for female odors) to the combination of the two stressors, suggesting positive carry-over effects. Nevertheless, full recovery to control levels was not observed. Altogether, this study indicates that future scenarios of ocean deoxygenation and warming have the potential to disrupt chemosensory-dependent mate-detection in amphipods, but also suggests possible behavioral adaptations. We call for greater research efforts on long-term impacts of ocean change on the behavioral and physiological processes of benthic coastal communities

A characterization of generalized multinomial coefficients related to the entropic chain rule

There is an asymptotic correspondence between the multiplicative relations among multinomial coefficients and the (additive) recursive property of Shannon entropy known as the chain rule. We show that both types of identities are manifestations of a unique algebraic construction: a 1-cocycle condition in information cohomology, an algebraic invariant of presheaves of modules on certain categories of observables. Depending on the coefficients, the 1-cocycles can be information measures (Shannon entropy, Tsallis α-entropy) or generalized (Fontené-Ward) multinomial coefficients. In each case the 1-cocycle condition encodes a system of functional equations. We obtain in particular a combinatorial analogue of the “fundamental equation of information theory”: a simple functional equation that uniquely characterizes the generalized binomial coefficients. The asymptotic correspondence mentioned above extends to any α-entropy and certain multinomial coefficients with compatible asymptotic behavior, shedding new light on the meaning of the chain rule and its deformations

Revisiting the Galactic X-Ray Binary MAXI J1631–479: Implications for High Inclination and a Massive Black Hole

X-ray spectroscopy of Galactic black hole binaries serves as a powerful tool to gain an overall understanding of the system. Not only can the properties of the accretion disk be studied in detail, the fundamental properties of the black hole such as spin and mass can also be measured. In this work we carry out a comprehensive spectral analysis of the X-ray binary MAXI J1631–479 using data from NICER and NuSTAR observatories. We trace the evolution of the accretion disk properties, such as density, ionization, and Fe abundance, as the source transitions from a disk-dominated soft state to a power-law-dominated hard intermediate state. As expected the disc ionization increased with hardness while the density and abundance (at solar values) remained unchanged. We provide strong constraints on the spin of the black hole (a > 0.996) and the inclination of the inner disk (50°–70°). We also use the soft-state NICER observations to constrain the black hole mass using distance estimates from optical observations. We find the probable mass of the black hole to be much higher than its X-ray binary counterparts with a conservative lower limit of 15 M_⊙ at 4.5 kpc

Polarization and variability of compact sources measured in Planck time-ordered data

This paper introduces a new Planck Catalog of Polarized and Variable Compact Sources (PCCS-PV) comprising 153 sources, the majority of which are extragalactic. The data include both the total flux density and linear polarization measured by Planck with frequency coverage from 30 to 353 GHz, and temporal spacing ranging from days to years. We classify most sources as beamed, extragalactic radio sources; the catalog also includes several radio galaxies, Seyfert galaxies, and Galactic and Magellanic Cloud sources, including H II regions and planetary nebulae. An advanced extraction method applied directly to the multifrequency Planck time-ordered data, rather than the mission sky maps, was developed to allow an assessment of the variability of polarized sources. Our analysis of the time-ordered data from the Planck mission, tod2flux, allowed us to catalog the time-varying emission and polarization properties for these sources at the full range of polarized frequencies employed by Planck, 30-353 GHz. PCCS-PV provides the time-and frequency-dependent, polarized flux densities for all 153 sources. To illustrate some potential applications of the PCCS-PV, we conducted preliminary comparisons of our measurements of selected sources with published data from other astronomical instruments. In summary, we find general agreement between the Planck and the Institut de Radioastronomie Millimétrique (IRAM) polarization measurements as well as with the Metsähovi 37 GHz values at closely similar epochs. These combined measurements also show the value of PCCS-PV results and the PCCS2 catalog for filling in missing spectral (or temporal) coverage and helping to define the spectral energy distributions of extragalactic sources. In turn, these results provide useful clues as to the physical properties of the sources

Constraining CaCO₃ Export and Dissolution With an Ocean Alkalinity Inverse Model

Ocean alkalinity plays a fundamental role in the apportionment of CO₂ between the atmosphere and the ocean. The primary driver of the ocean's vertical alkalinity distribution is the formation of calcium carbonate (CaCO₃) by organisms at the ocean surface and its dissolution at depth. This so-called “CaCO₃ counterpump” is poorly constrained, however, both in terms of how much CaCO₃ is exported from the surface ocean, and at what depth it dissolves. Here, we created a steady-state model of global ocean alkalinity using Ocean Circulation Inverse Model transport, biogeochemical cycling, and field-tested calcite and aragonite dissolution kinetics. We find that limiting CaCO₃ dissolution to below the aragonite and calcite saturation horizons cannot explain excess alkalinity in the upper ocean, and that models allowing dissolution above the saturation horizons best match observations. Linking dissolution to organic matter respiration, or imposing a constant dissolution rate both produce good model fits. Our best performing models require export between 1.1 and 1.8 Gt PIC y⁻¹ (from 73 m), but all converge to 1.0 Gt PIC y⁻¹ export at 279 m, indicating that both high- and low-export scenarios can match observations, as long as high export is coupled to high dissolution in the upper ocean. These results demonstrate that dissolution is not a simple function of seawater CaCO₃ saturation (Ω) and calcite or aragonite solubility, and that other mechanisms, likely related to the biology and ecology of calcifiers, must drive significant dissolution throughout the water column

Diastereoselectivity Switch During Alkene Reductions: Diastereodivergent Syntheses of Molecular Fossils via MHAT or Homogeneous Catalytic Hydrogenation Reactions

Sixteen geosterane derivatives were synthesized in up to 57 % overall yields in four steps harnessing the olefin cross-metathesis (OCM) and Metal hydride H atom transfer (MHAT) or homogeneous hydrogenation reactions as key steps. Drawing on this strategy, the diastereomeric ratio (d. r.) reached up to 24 : 1 for the thermodynamic isomer and 7 : 1 for the other isomer in the hydrogenation step. In a geological sample from northeast Brazil, we confirmed the putative structures previously assumed as methyl 2-(3α-5αH-cholestan) acetate, methyl 2-(3β-5αH-cholestan)acetate, and methyl 6-(3β-5αH-cholestan)hexanoate, as well three new molecular fossils of approximately 120 million years old. We also proved the migration marking ability of those carboxylic acids derived from forerunner geosteranes during an oil migration event, which suggests their aptitudes as molecular odometers. Our approach demonstrated swiftness and effectiveness in preparing a molecular library of geological biomarkers would also be appropriate to generate stereochemical diversity in molecular libraries for medicinal chemistry and natural product anticipation

On the Optimality and Convergence Properties of the Iterative Learning Model Predictive Controller

In this technical article, we analyze the performance improvement and optimality properties of the learning model predictive control (LMPC) strategy for linear deterministic systems. The LMPC framework is a policy iteration scheme where closed-loop trajectories are used to update the control policy for the next execution of the control task. We show that, when a linear independence constraint qualification (LICQ) condition holds, the LMPC scheme guarantees strict iterative performance improvement and optimality, meaning that the closed-loop cost evaluated over the entire task converges asymptotically to the optimal cost of the infinite-horizon control problem. Compared to previous works, this sufficient LICQ condition can be easily checked, it holds for a larger class of systems and it can be used to adaptively select the prediction horizon of the controller, as demonstrated by a numerical example

Quantum Gravity in the Lab. I. Teleportation by Size and Traversable Wormholes

With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the recent traversable-wormhole constructions of Gao et al. [J. High Energy Phys., 2017, 151 (2017)] and Maldacena et al. [Fortschr. Phys., 65, 1700034 (2017)]: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of teleportation by size to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semiclassical holographic wormhole corresponds to a rather special property of the operator-size distribution that we call size winding. For more general systems (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable-wormhole phenomenon. In addition, a form of signaling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole but, rather, to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations that are feasible with current technology in two experimental platforms: Rydberg-atom arrays and trapped ions

Detectors in weakly-coupled field theories

We initiate a study of asymptotic detector operators in weakly-coupled field theories. These operators describe measurements that can be performed at future null infinity in a collider experiment. In a conformal theory they can be identified with light-ray operators, and thus have a direct relation to the spectrum of the theory. After a general discussion of the underlying physical picture, we show how infrared divergences of general detector operators can be renormalized in perturbation theory, and how they give rise to detector anomalous dimensions. We discuss in detail how this renormalization can be performed at the intersections of the Regge trajectories where non-trivial mixing occurs, which is related to the poles in anomalous dimensions at special values of spin. Finally, we discuss novel horizontal trajectories in scalar theories and show how they contribute to correlation functions. Our calculations are done in the example of ϕ⁴ theory in d = 4 − ϵ dimensions, but the methods are applicable more broadly. At the Wilson-Fisher fixed point our results include an explicit expression for the Pomeron light-ray operator at two loops, as well as a prediction for the value of the Regge intercept at five loops