Due to Gödel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments—Warren [43] and Murzi and Topey [30]—for the idea that the natural deduction rules for the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s [19] local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e., non-compact. Consequently, I reconsider the use of the $\omega $-rule and I show that the addition of the $\omega $-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement.

Past human population dynamics play a key role in integrated models of understanding socio-ecological change over time. However, little analysis on this issue has been carried out for the prehistoric societies in the Lower Danube and Eastern Balkans area. Here, we use summed probability distributions of radiocarbon dates to investigate potential regional and local variation population dynamics. Our study adopts a formal model-testing approach to the fifth millennium BC archaeological radiocarbon record, performing a region-wide, comparative analysis of the demographic trajectories of the area along lower Danube River. We follow the current framework of theoretical models of population growth and perform global and regional significance and spatial permutation tests on the data. Specifically, we investigate whether populations on both sides of the Danube follow a logistic pattern of steady growth, followed by a major decline over time. Finally, our analysis of local-scale growth investigates whether considerable heterogeneity or homogeneity within the region may be observed over the time span considered here. The results show both similarities and differences in the population trends across the area. Our findings are showcased in relation to the cultural characteristics of the region’s 5th millennium BC societies, and future research directions are also suggested.

If water megamaser disk activity is intimately related to the circumnuclear activity from accreting supermassive black holes, a thorough understanding of the co-evolution of galaxies with their central black holes should consider the degree to which the maser production correlates with traits of their host galaxies. This contribution presents an investigation of multiwavelength nuclear and host properties of galaxies with and without water megamasers, that reveals a rather narrow multi-dimensional parameter space associated with the megamaser emission. This “goldilocks” region embodies the availability of gas, the degree of dusty obscuration and reprocessing of the central emission, the black hole mass, and the accretion rate, suggesting that the disk megamaser emission in particular is linked to a short-lived phase in the intermediate-mass galaxy evolution, providing new tools for both 1) further constraining the growth process of the incumbent AGN and its host galaxy, and 2) significantly boosting the maser disk detection by efficiently confining the 22 GHz survey parameters.

In this paper we present a high repetition rate experimental platform for examining the spatial structure and evolution of Biermann-generated magnetic fields in laser-produced plasmas. We have extended the work of prior experiments, which spanned over millimeter scales, by spatially measuring magnetic fields in multiple planes on centimeter scales over thousands of laser shots. Measurements with magnetic flux probes show azimuthally symmetric magnetic fields that range from 60 G at 0.7 cm from the target to 7 G at 4.2 cm from the target. The expansion rate of the magnetic fields and evolution of current density structures are also mapped and examined. Electron temperature and density of the laser-produced plasma are measured with optical Thomson scattering and used to directly calculate a magnetic Reynolds number of $1.4\times {10}^4$ , confirming that magnetic advection is dominant at $\ge 1.5$ cm from the target surface. The results are compared to FLASH simulations, which show qualitative agreement with the data.

Substantial progress has been made in the standardization of nomenclature for paediatric and congenital cardiac care. In 1936, Maude Abbott published her Atlas of Congenital Cardiac Disease, which was the first formal attempt to classify congenital heart disease. The International Paediatric and Congenital Cardiac Code (IPCCC) is now utilized worldwide and has most recently become the paediatric and congenital cardiac component of the Eleventh Revision of the International Classification of Diseases (ICD-11). The most recent publication of the IPCCC was in 2017. This manuscript provides an updated 2021 version of the IPCCC.

The International Society for Nomenclature of Paediatric and Congenital Heart Disease (ISNPCHD), in collaboration with the World Health Organization (WHO), developed the paediatric and congenital cardiac nomenclature that is now within the eleventh version of the International Classification of Diseases (ICD-11). This unification of IPCCC and ICD-11 is the IPCCC ICD-11 Nomenclature and is the first time that the clinical nomenclature for paediatric and congenital cardiac care and the administrative nomenclature for paediatric and congenital cardiac care are harmonized. The resultant congenital cardiac component of ICD-11 was increased from 29 congenital cardiac codes in ICD-9 and 73 congenital cardiac codes in ICD-10 to 318 codes submitted by ISNPCHD through 2018 for incorporation into ICD-11. After these 318 terms were incorporated into ICD-11 in 2018, the WHO ICD-11 team added an additional 49 terms, some of which are acceptable legacy terms from ICD-10, while others provide greater granularity than the ISNPCHD thought was originally acceptable. Thus, the total number of paediatric and congenital cardiac terms in ICD-11 is 367. In this manuscript, we describe and review the terminology, hierarchy, and definitions of the IPCCC ICD-11 Nomenclature. This article, therefore, presents a global system of nomenclature for paediatric and congenital cardiac care that unifies clinical and administrative nomenclature.

The members of ISNPCHD realize that the nomenclature published in this manuscript will continue to evolve. The version of the IPCCC that was published in 2017 has evolved and changed, and it is now replaced by this 2021 version. In the future, ISNPCHD will again publish updated versions of IPCCC, as IPCCC continues to evolve.

The aim of this research communication was to examine the effect of dietary supplementation with wheat-based dried distillers’ grains with solubles (DDGS), a by-product of bioethanol production, on yield, composition, and fatty acid (FA) profile of ewe milk. Forty-five purebred mid-lactating Chios ewes (average milk yield 2.23 kg/d in 96 ± 5 d in lactation) were offered three iso-nitrogenous and iso-energetic diets (15 animals per diet) for a 10 d adaptation period followed by a 5-week recording and sampling period. The diets contained 0, 6, and 12% DDGS on DM basis for the DG0, DG6, and DG12 treatment, respectively, as a replacement of concentrate mix, whilst concentrate-to-forage ratio remained at 60:40 in all treatments. Individual milk yield, milk composition, and FA profile were recorded weekly and analyzed using a complete randomized design with repeated measurements. No significant differences were observed among groups concerning dry matter intake (overall mean of 2.59 kg/d), milk yield or 6% fat-corrected milk and milk protein percentage or protein yield. Milk fat percentage was decreased in the DG12 (4.76%) compared to DG0 (5.69%) without, however, significantly affecting the daily output of milk fat. The concentration of all major saturated FA between C4:0 to C16:0 was reduced, whereas long-chain (>16 carbons), mono-unsaturated and poly-unsaturated FAs were increased in the milk of DDGS groups. Among individual FA, increments of oleic acid and C18:1 trans-monoenes like C18:1 trans-10 and C18:1 trans-11 were demonstrated in DG12 group, whereas linoleic and conjugated linoleic acid (CLA cis-9, trans-11) were elevated in both DDGS groups compared to control. Changes in FA profile resulted in a decline in the atherogenic index of milk by 20% and 35% in DG6 and DG12 treatments, respectively, compared with control. In conclusion, feeding DDGS to dairy ewes increased the levels of unsaturated FA that are potentially beneficial for human health without adversely affecting milk, protein or fat yield.

Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators and parametric instabilities from temporal mean flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in simplified physical models. Whether the flow follows any or a combination of them remains elusive. Here, we evaluate the linear mechanisms responsible for the energy transfer from the streamwise-averaged mean flow ($\boldsymbol {U}$) to the fluctuating velocities ($\boldsymbol {u}'$). To that end, we use cause-and-effect analysis based on interventions: manipulation of the causing variable leads to changes in the effect. This is achieved by direct numerical simulation of turbulent channel flows at low Reynolds number, in which the energy transfer from $\boldsymbol {U}$ to $\boldsymbol {u}'$ is constrained to preclude a targeted linear mechanism. We show that transient growth is sufficient for sustaining realistic wall turbulence. Self-sustaining turbulence persists when exponential instabilities, neutral modes and parametric instabilities of the mean flow are suppressed. We further show that a key component of transient growth is the Orr/push-over mechanism induced by spanwise variations of the base flow. Finally, we demonstrate that an ensemble of simulations with various frozen-in-time $\boldsymbol {U}$ arranged so that only transient growth is active, can faithfully represent the energy transfer from $\boldsymbol {U}$ to $\boldsymbol {u}'$ as in realistic turbulence. Our approach provides direct cause-and-effect evaluation of the linear energy-injection mechanisms from $\boldsymbol {U}$ to $\boldsymbol {u}'$ in the fully nonlinear system and simplifies the conceptual model of self-sustaining wall turbulence.

In the problem of horizontal convection a non-uniform buoyancy, $b_{s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\boldsymbol{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\boldsymbol{J}\boldsymbol{\cdot }\unicode[STIX]{x1D735}b_{s}}=-\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$; the overbar denotes a space–time average over the top surface, angle brackets denote a volume–time average and $\unicode[STIX]{x1D705}$ is the molecular diffusivity of buoyancy $b$. This connection between $\boldsymbol{J}$ and $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number. We investigate transient effects and show that $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ equilibrates more rapidly than other global averages, such as the averaged kinetic energy and bottom buoyancy. We show that $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ is the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux through the top surface. This leads to an equivalent ‘surface Nusselt number’, defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{s}(x,y)$. In experimental situations it is easier to evaluate the surface entropy flux, rather than the volume integral of $|\unicode[STIX]{x1D735}b|^{2}$ demanded by $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$.

We present a new experimental platform for studying laboratory astrophysics that combines a high-intensity, high-repetition-rate laser with the Large Plasma Device at the University of California, Los Angeles. To demonstrate the utility of this platform, we show the first results of volumetric, highly repeatable magnetic field and electrostatic potential measurements, along with derived quantities of electric field, charge density and current density, of the interaction between a super-Alfvénic laser-produced plasma and an ambient, magnetized plasma.

Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow $U(t)$ and smaller-scale macroturbulence characterized by standing and transient eddies. The large-scale flow $U$ is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineate the main flow regimes and the dependence of the time average of $U$ on parameters such as the planetary potential vorticity (PV) gradient $\unicode[STIX]{x1D6FD}$ and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow $U$ in the limiting cases of weak and strong forcing. If $\unicode[STIX]{x1D6FD}$ is significantly smaller than the topographic PV gradient, the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain, the flow is weak and thus the large-scale flow $U$ is an unoccupied mean. If $\unicode[STIX]{x1D6FD}$ is comparable to, or larger than, the topographic PV gradient, then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case, there is an ‘eddy saturation’ regime in which $U$ is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between the topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals, we show that as the strength of the wind stress increases, the flow transitions from a regime in which the form stress balances most of the wind stress to a regime in which the form stress is very small and large transport ensues.

Radiocarbon-dated macrofossils are used to document Holocene treeline history across northern Russia (including Siberia). Boreal forest development in this region commenced by 10,000 yr B.P. Over most of Russia, forest advanced to or near the current arctic coastline between 9000 and 7000 yr B.P. and retreated to its present position by between 4000 and 3000 yr B.P. Forest establishment and retreat was roughly synchronous across most of northern Russia. Treeline advance on the Kola Peninsula, however, appears to have occurred later than in other regions. During the period of maximum forest extension, the mean July temperatures along the northern coastline of Russia may have been 2.5° to 7.0°C warmer than modern. The development of forest and expansion of treeline likely reflects a number of complimentary environmental conditions, including heightened summer insolation, the demise of Eurasian ice sheets, reduced sea-ice cover, greater continentality with eustatically lower sea level, and extreme Arctic penetration of warm North Atlantic waters. The late Holocene retreat of Eurasian treeline coincides with declining summer insolation, cooling arctic waters, and neoglaciation.

The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in a variety of physical systems. An SSD is a dynamical system that evolves a representation of the statistical state of the system. An example of an SSD is the second-order cumulant closure referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence, and specifically the emergence and maintenance of the roll/streak structure. S3T comprises a coupled set of equations for the streamwise mean and perturbation covariance, in which nonlinear interactions among the perturbations has been removed, restricting nonlinearity in the dynamics to that of the mean equation and the interaction between the mean and perturbation covariance. In this work, this quasi-linear restriction of the dynamics is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high Reynolds numbers in a closely related dynamical system, referred to as the restricted nonlinear (RNL) system. Simulations using this RNL system reveal that the essential features of wall-turbulence dynamics are retained. Consistent with previous analyses based on the S3T version of SSD, the RNL system spontaneously limits the support of its turbulence to a small set of streamwise Fourier components, giving rise to a naturally minimal representation of its turbulence dynamics. Although greatly simplified, this RNL turbulence exhibits natural-looking structures and statistics, albeit with quantitative differences from those in direct numerical simulations (DNS) of the full equations. Surprisingly, even when further truncation of the perturbation support to a single streamwise component is imposed, the RNL system continues to self-sustain turbulence with qualitatively realistic structure and dynamic properties. RNL turbulence at the Reynolds numbers studied is dominated by the roll/streak structure in the buffer layer and similar very large-scale structure (VLSM) in the outer layer. In this work, diagnostics of the structure, spectrum and energetics of RNL and DNS turbulence are used to demonstrate that the roll/streak dynamics supporting the turbulence in the buffer and logarithmic layer is essentially similar in RNL and DNS.

Thin films of organic semiconductor PEDOT:PSS deposited onto silicon and fusedsilica substrates. These films were then treated with sulfuric acid(H2SO4) for various amounts of time (i.e., 10, 20, 40,60, and 80 minutes). Preliminary results obtained with FT-IR, UV-VIS, and VanDerPauw conductivity methods suggest that the H2SO4removes the PSS isonomer from the PEDOT:PSS system. This PSS removal alsoinduces a decrease in film thickness.