The helicity is a topological conserved quantity of the Euler equations which imposes significant constraints on the dynamics of vortex lines. In the compressible setting, the conservation law holds only under the assumption that the pressure is barotropic. Let us consider a volume $V$ containing a compressible fluid with density $\rho$, velocity field $\textbf{u}$ and vorticity $\boldsymbol{\omega}$. We show that by introducing a new definition of helicity density $h_{\rho }=(\rho {\boldsymbol {u}})\cdot \mbox {curl}\,(\rho {\boldsymbol {u}})$ the barotropic assumption on the pressure can be removed, although ${\int _{V}} h_{\rho }{\rm d}V$ is no longer conserved. However, we show for the non-barotropic compressible Euler equations that the new helicity density $h_{\rho }$ obeys an entropy-type relation (in the sense of hyperbolic conservation laws) whose flux ${\boldsymbol {J}}_{\rho }$ contains all the pressure terms and whose source involves the potential vorticity $q = \boldsymbol{\omega} \cdot \nabla \rho$. Therefore, the rate of change of ${\int _{V}} h_{\rho }{\rm d}V$ no longer depends on the pressure and is easier to analyse, as it depends only on the potential vorticity and kinetic energy as well as $\mbox {div}\,{\boldsymbol {u}}$. This result also carries over to the inhomogeneous incompressible Euler equations for which the potential vorticity $q$ is a material constant. Therefore, $q$ is bounded by its initial value $q_{0}=q({\boldsymbol {x}},\,0)$, which enables us to define an inverse resolution length scale $\lambda _{H}^{-1}$ whose upper bound is found to be proportional to $\|q_{0}\|_{\infty }^{2/7}$. In a similar manner, we also introduce a new cross-helicity density for the ideal non-barotropic magnetohydrodynamic (MHD) equations.

Objectives/Goals: Radiation nephropathy results in morbidity and mortality in patients receiving cancer treatment. In addition, low birth weight and low nephron number are associated with increased risk for chronic kidney disease. This study examined the development and severity of radiation-induced renal hemodynamic dysfunction in a low renal mass mouse model. Methods/Study Population: Male mice (C57Bl/6, 8–12-weeks) were used to determine a suitable radiation dose regimen. Mice were subjected to fractionated bilateral kidney irradiation with 5–6 fractions of an X-ray dose of 0, 6, 8, and 10 Gy at 24-hr intervals using a CT-image-guided irradiator. Body weight and mortality were monitored for 5 weeks in mice. In a separate set of experiments, the low renal mouse model, ROP Os/+, and their normal counterpart, ROP +/+ mice were subjected to 5 fractionated bilateral kidney irradiations at 24-hr intervals with an X-ray dose of 6 Gy. Renal blood flow was assessed from renal artery resistive index (RRI) over 5 weeks post-irradiation using an ultrasound system. Transcutaneous measurement of FITC-sinistrin clearance was used to determine glomerular filtration rate (GFR). Results/Anticipated Results: The C57Bl/6 mice that received 5–6 fractions of 8 and 10 Gy had more than 50% mortality, while 100% of the mice exposed to 5 fractions of 6 Gy survived for 5 weeks. Body weight was also significantly decreased in mice exposed to 5 or 6 fractions of 8 or 10 but not 6 Gy radiation. Nonirradiated C57Bl/6, ROP +/+, and ROP Os/+ mice had similar baseline GFR and RRI. Irradiation of 5 fractions at 6 Gy decreased GFR and increased RRI in C57Bl/6 and ROP +/+ mice. Interestingly, following 5 fractions at 6 Gy irradiation ROP Os/+ mice had 25% lower GFR than wild-type ROP +/+ mice (946.3 ± 50.3 vs. 1232.9 ± 69.3 µL/min/100g BW, p Discussion/Significance of Impact: Our study determined a suitable fractionated bilateral kidney irradiation dose regimen to evaluate radiation nephropathy. Data demonstrated that fractionated bilateral kidney irradiation leads to decreased renal hemodynamics in mice. We also demonstrated that irradiation caused greater renal hemodynamic dysfunction in low renal mass mice.

Objectives/Goals: Digital recruitment can improve participant engagement in medical research, but its potential to introduce demographic and socioeconomic biases is unclear. This study investigates pathways participants took during a digital recruitment workflow in neurology, examining potential associations with socioeconomic and demographic factors. Methods/Study Population: As part of an ongoing study aiming to remotely capture speech from patients with neurologic disease, most participants seen in neurology on our campus are invited to complete a self-administered speech examination. We exported participant data from Epic (semi-automated identification and invitation), Qualtrics (eligibility screening), the participant tracking database (consent), and the recording platform (completion) for March to July 2024. Data visualization was performed using a Sankey diagram. Socioeconomic status was assessed using the housing-based socioeconomic status (HOUSES) index and area deprivation index (ADI) national rank. Kruskal–Wallis and Wilcoxon rank-sum tests were used to compare the median age, socioeconomic indices, and time taken to reach different steps of the study. Results/Anticipated Results: Of the 5846 invited participants, 57% were from urban areas, 23% from rural areas, and 20% from urban clusters. Most did not read/respond (2739) or declined (1749) the initial invitation via Epic. Of the 1358 interested participants, 415 completed the study. Participants from urban areas completed enrollment steps faster than those from rural areas and urban clusters, though the variance was large (42.6 ± 41.4 days vs. 50.6 ± 42.2 days and 50 ± 43.9 days, respectively; p  =  0.030). Female participants took longer to complete enrollment than males (48.7 ± 44 days vs. 40.5 ± 38.8 days; p  =  0.026). Participants who successfully finished the study had significantly lower ADI national ranks compared to other common pathways (40.6 ± 19; p  =  0.0021). No associations were found with the HOUSES indices. Discussion/Significance of Impact: Our findings support differences in participant engagement, with urban participants and males more likely to complete enrollment steps. Those who finished the study were less disadvantaged suggesting potential bias in digital recruitment. These findings can inform strategies to improve digital recruitment in neurology research.

One of the earliest discoveries of Permo-Carboniferous terrestrial vertebrates in North America occurred in 1875 along Horseshoe Bend, a cutbank on the Salt Fork of the Vermilion River west of Danville, Vermilion County, east-central Illinois. The discovery was soon eclipsed by the description of similar but much more complete remains from the Lower Permian of Texas in 1878. The deposit itself was obliterated by slumping and erosion in the earliest 1900s and has not been collected since despite repeated efforts. Previously unreported outcrop records and subsurface data indicate that the deposit originated as a paleochannel fill in the Inglefield Sandstone Member of the Patoka Formation, which underlies the Macoupin Limestone Member (early Missourian Stage of the Midcontinent, early Kasimovian Stage of global Carboniferous time scale). In addition to aquatic to terrestrial tetrapods, teeth of lungfishes (Sagenodus Owen, 1867, Conchopoma Cope, 1877a, Gnathorhiza Cope, 1883a) and teeth, occipital spines, and coprolites of a xenacanth shark (Orthacanthus Agassiz, 1838) are known from Horseshoe Bend. The teeth of the marine petalodont shark Janassa Münster, 1839, also are present in the collection but presumed to have been derived from one of the beds on the cutbank that produced brackish to marine invertebrate fossils. Alhough not diverse, the tetrapod assemblage is significant in that it contains the oldest diplocaulid amphibian (Diplocaulus salamandroides Cope, 1877a), fragmentary remains of the oldest diadectid and limnoscelid stem reptiles, and possibly the oldest captorhinid eureptile, all of which have not been adequately described. The ophiacodontid synapsid Clepsydrops Cope, 1875, is the most common fossil at Danville, which could be an artifact of primitive collecting methods that did not promote the recovery of articulated material. An accurate stratigraphic placement of the Horseshoe Bend deposit and a review of other late Carboniferous tetrapod localities reveals that this important Illinois locality combines an overlooked vanguard of terrestrial taxa regarded as Permo-Carboniferous (Kasimovian-Asselian) and amphibious to aquatic forms known from older, Moscovian deposits.

Japanese stiltgrass is one of the most troublesome invasive weed species in the eastern United States. Strategies for Japanese stiltgrass control in managed lawns are limited since most previous research was conducted in forest understories or golf course natural areas. Eight field experiments were conducted in Virginia from 2014 to 2019 to evaluate the response of Kentucky bluegrass, tall fescue, and Japanese stiltgrass to selective herbicides traditionally marketed for cool-season turfgrass. Only mesotrione-containing treatments transiently injured tall fescue 15 to 25% at 2 wk after treatment (WAT). Fenoxaprop at 35 g ha-1 or higher rates controlled Japanese stiltgrass ≥ 90%, reduced relative cover to <15% compared to nontreated and shoot density to ≤ 6 shoots m-2, respectively, at 8 WAT. Sequential application of topramezone at 3-wk intervals at 27 g ha-1, single application of topramezone at 54 g ha-1 alone or with triclopyr controlled Japanese stiltgrass ≥ 80% and reduced relative weed cover and shoot density to ≤ 22% and < 35 shoots m-2, respectively. Fenoxaprop at 0.25 of the labeled rate for annual grass control in lawns and topramezone-based programs selectively controlled Japanese stiltgrass without injuring tall fescue. Fluazifop at 53 g ha-1 injured Kentucky bluegrass 25% and reduced digitally assessed turf cover by 20% at 4 WAT, but turfgrass recovered by 6 WAT. Reduced rates of fluazifop controlled Japanese stiltgrass 85% and reduced weed shoot density to < 20 shoots m-2 and relative cover to < 20% at 8 WAT. A premix of dicamba, fenoxaprop, and fluroxypyr did not injure Kentucky bluegrass but controlled Japanese stiltgrass ≥ 92% and reduced the relative weed cover and shoot density to ≤ 7% and ≤ 5 shoots m-2, respectively, at 8 WAT. Our research provides herbicide options to practitioners to manage Japanese stiltgrass in Kentucky bluegrass and tall fescue lawns.

We carry out two experiments to test a model of herd behaviour based on the work of Banerjee (Quarterly Journal of Economics, CVII, 797-817,1992). He shows that herding occurs as a result of people observing the actions of others and using this information in their own decision rule. In our experiments herding does not occur as frequently as Banerjee predicts. Contrary to his results, the subjects’ behaviour appears to depend on the probabilities of receiving a signal and of this signal being correct. Furthermore, Banerjee finds that the pattern of decision making over a number of rounds of the game is volatile whereas we find that decision making is volatile within rounds.

In many experiments, particularly individual choice experiments, experimenters ask many questions to the subjects and use the random lottery incentive mechanism to give an incentive to the subjects. That is, the experimenter, at the end of the experiment, picks just one of the questions, plays out that question, and pays the subject on the basis of this one question. The idea is that subjects should separate the various questions and reply to each as if it were a separate question—in isolation from all the other questions in the experiment. This procedure is methodologically sound if the subjects behave in accordance with Expected Utility (EU) theory, since this theory says that the best procedure for the subjects is to separate the various questions. However, if there is any doubt as to whether the subjects obey EU theory, and particularly if the experiment is designed to test whether the behaviour of the subjects is in accordance with EU, this incentive mechanism is open to criticism. Indeed many referees use this argument against the research. The response that the subjects may not respect EU, yet still separate the various questions, is obviously open to objection and generally it is not clear whether this response is valid or not. There have been two direct tests of this separation hypothesis (by Starmer and Sugden (1991) and by Cubitt et al. (1998), which suggest that it is valid, but further evidence is required. This paper provides a further, stronger, test of this hypothesis: we confront the two stories—(1) that the subjects answer the various questions separately, and (2) that the subjects respond to the experiment as a whole—using experimental data from an experiment in which the random lottery incentive mechanism was used. Our analysis shows that it would appear that subjects do answer as if they were separating the questions. This should be considered reassuring for those experimenters who use the random lottery incentive mechanism.

We report the results of an experimental investigation of a key axiom of economic theories of dynamic decision making—namely, that agents plan. Inferences from previous investigations have been confounded with issues concerning the preference functionals of the agents. Here, we present an innovative experimental design which is driven purely by dominance: if preferences satisfy dominance, we can infer whether subjects are planning or not. We implement three sets of experiments: the first two (the Individual Treatments) in which the same player takes decisions both in the present and the future; and the third (the Pairs Treatment) in which different players take decisions at different times. The two Individual treatments differed in that, in one, the subjects played sequentially, while, in the other, the subjects had to pre-commit to their future move. In all contexts, according to economic theory, the players in the present should anticipate the decision of the player in the future. We find that over half the participants in all three experimental treatments do not appear to be planning ahead; moreover, their ability to plan ahead does not improve with experience, except possibly when we force subjects to pre-commit to their future decision. These findings identify an important lacuna in economic theories, both for individual behaviour and for behaviour in games.

We use experimental methods to evaluate a simplified interbank market. The design is a laboratory adaptation of the analysis of interbank market fragility by Allen and Gale (J Eur Econ Assoc 2:1015–1048), and features symmetric banks who allocate deposit endowments between cash and illiquid assets prior to the incidence of a shock. Following the shock liquidity-deficient banks trade assets for cash. Treatments include variations in the shock type, as well as alterations in the range of permissible asset prices. Consistent with Allen and Gale, we find that while interbank trading substantially increases investment activity, the markets are frequently characterized by price variability and a stochastic distribution of investment outcomes.

Countless experimental studies have shown that markets converge quickly and efficiently to the competitive outcome under many trading institutions, particularly the double auction mechanism. This creates difficulties for Keynesian stories of unemployment creation—which suggest a noncompetitive outcome in an essentially competitive world. Such stories were popular in the late 1960s and 1970s. One of these stories—the dual decision hypothesis of Clower—was seen then as the beginning of a story of unemployment. This article reports the results of an experiment designed to test this hypothesis. Specifically, we set up an experiment in which there are two sequential double-auction markets, in the first of which one good (labour) is traded, after which the second market (goods) is opened and the second good traded. We compare the outcome of our experiment with that of the competitive theory. One general finding is that not enough trade takes place in the two markets. In other words, the usual finding that competitive equilibrium is achieved in double-auction markets is not replicated in this sequential setting.

Inspired by Clower’s conjecture that the necessity of trading through money in monetised economies might hinder convergence to competitive equilibrium, and hence, for example, cause unemployment, we experimentally investigate behaviour in markets where trading has to be done through money. In order to evaluate the properties of these markets, we compare their behaviour to behaviour in markets without money, where money cannot intervene. As the trading mechanism might be a compounding factor, we investigate two kinds of market mechanism: the double auction, where bids, asks and trades take place in continuous time throughout a trading period; and the clearing house, where bids and asks are placed once in a trading period, and which are then cleared by an aggregating device. We thus have four treatments, the pairwise combinations of non-monetised/monetised trading with double auction/clearing house. We find that: convergence is faster under non-monetised trading, implying that the necessity of using money to facilitate trade hinders convergence; that monetised trading is noisier than non-monetised trading; and that the volume of trade and realised surpluses are higher with the double auction than the clearing house. As far as efficiency is concerned, monetised trading lowers both informational and allocational efficiency, and while the double auction outperforms the clearing house in terms of allocational efficiency, the clearing house is marginally better than the double auction in terms of informational efficiency when trade is through money. Crucially we confirm the conjecture that inspired these experiments: that the necessity to use money in trading hinders convergence to competitive equilibrium, lowers realised trades and surpluses, and hence may cause unemployment.

There is an odd contradiction about much of the empirical (experimental) literature: The data is analysed using statistical tools which presuppose that there is some noise or randomness in the data, but the source and possible nature of the noise are rarely explicitly discussed. This paper argues that the noise should be brought out into the open, and its nature and implications openly discussed. Whether the statistical analysis involves testing or estimation, the analysis inevitably is built upon some assumed stochastic structure to the noise. Different assumptions justify different analyses, which means that the appropriate type of analysis depends crucially on the stochastic nature of the noise. This paper explores such issues and argues that ignoring the noise can be dangerous.

Much experimental effort has been expended in attempts to establish the relative superiority of Expected Utility theory and the many recently-developed alternatives as descriptions of the behaviour of subjects in risky choice decision problems. The cumulative evidence shows clearly that there is a great deal of noise in the experimental data, which makes it difficult to identify the ‘best’ description of such behaviour. This paper reports on an experiment which seeks to determine whether such noise is relatively transitory and decays with experience and repetition, and thus whether a clearly ‘best’ theory emerges as a result of such repetition. We find that for some subjects this does indeed appear to be the case, while for other subjects the noise remains high and the identification of the underlying preference function remains difficult.