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We resolve the multiple images of the binary-lens microlensing event ASASSN-22av using the GRAVITY instrument of the Very Large Telescope Interferometer (VLTI). The light curves show weak binary perturbations, complicating the analysis, but the joint modeling with the VLTI data breaks several degeneracies, arriving at a strongly favored solution. Thanks to precise measurements of angular Einstein radius \theta_E = 0.724 +/- 0.002 mas and microlens parallax, we determine that the lens system consists of two M dwarfs with masses of M_1 = 0.258 +/- 0.008 M_sun and M_2 = 0.130 +/- 0.007 M_sun, a projected separation of r_\perp = 6.83 +/- 0.31 AU and a distance of D_L = 2.29 +/- 0.08 kpc. The successful VLTI observations of ASASSN-22av open up a new path for studying intermediate-separation (i.e., a few AUs) stellar-mass binaries, including those containing dark compact objects such as neutron stars and stellar-mass black holes., Comment: Accepted by ApJ. See the ancillary file for animation associated with Fig. 8

Airway constriction and blockage in obstructive lung diseases cause ventilation heterogeneity and create barriers to effective drug deposition. Established computational particle-deposition models have not accounted for these impacts of disease. We present a new particle-deposition model that calculates ventilation based on the resistance of each airway, such that ventilation responds to airway constriction. The model incorporates distal airway constrictions representative of cystic fibrosis, allowing us to investigate the resulting impact on patterns of deposition. Unlike previous models, our model predicts how constrictions affect deposition in airways throughout the lungs, not just in the constricted airways. Deposition is reduced in airways directly distal and proximal to constrictions. When constrictions are clustered together, central-airways deposition can increase significantly in regions away from constrictions, but distal-airways deposition in those regions remains largely unchanged. We use our model to calculate lung clearance index (LCI), a clinical measure of ventilation heterogeneity, after applying constrictions of varying severities in one lobe. We find an increase in LCI coinciding with significantly reduced deposition in the affected lobe. Our results show how the model provides a framework for development of computational tools that capture the impacts of airway disease, which could significantly affect predictions of regional dosing., Comment: 24 pages, 9 figures

We present the results from a complex study of an eclipsing O-type binary (Aa+Ab) with the orbital period $P_{A}=3.2254367$ days, that forms part of a higher-order multiple system in a configuration (A+B)+C. We derived masses of the Aa+Ab binary $M_{1}= 19.02 \pm 0.12 \,M_\odot$, $M_{2}= 17.50 \pm 0.13 \,M_\odot$, radii $R_{1}= 7.70 \pm 0.05 \,R_\odot$, $R_{2}= 6.64 \pm 0.06 \,R_\odot$, and temperatures $T_1 = 34250 \pm 500 $ K, $T_2 = 33750 \pm 500 $ K. From the analysis of radial velocities, we found a spectroscopic orbit of A in the outer A+B system with $P_{A+B}=195.8$ days ($P_{A+B}/P_{A}\approx 61$). In the O-C analysis, we confirmed this orbit and found another component orbiting the A+B system with $P_{AB+C}=2550$ days ($P_{AB+C}\,/P_{A+B}\approx 13$). From the total mass of the inner binary and its outer orbit, we estimated the mass of the third object, $M_B \gtrsim 10.7 M_\odot$. From the light-travel time effect fit to the O-C data, we obtained the limit for the mass of the fourth component, $M_C \gtrsim 7.3 M_\odot$. These extra components contribute to about 20% to 30% (increasing with wavelength) of the total system light. From the comparison of model spectra with the multiband photometry, we derived a distance modulus of 18.59 $\pm$ 0.06 mag, a reddening of 0.16 $\pm$ 0.02 mag, and an $R_V$ of $3.2$. This work is part of our ongoing project, which aims to calibrate the surface brightness-color relation for early-type stars., Comment: 15 pages, 14 figures, 3 tables, accepted for publication in The Astrophysical Journal

The growing number of Milky Way satellites detected in recent years has introduced a new focus for stellar abundance analysis. Abundances of stars in satellites have been used to probe the nature of these systems and their chemical evolution. However, for most satellites, only centrally located stars have been examined. This paper presents an analysis of three stars in the Tucana V system, one in the inner region and two at $\sim$10\arcmin\ (7--10 half-light radii) from the center. We find a remarkable chemical diversity between the stars. One star exhibits enhancements in rapid neutron-capture elements (an $r$-I star), and another is highly enhanced in C, N, and O but with low neutron-capture abundances (a CEMP-no star). The metallicities of the stars analyzed span more than 1~dex from $\mathrm{[Fe/H]}=-3.55$ to $-2.46$. This, combined with a large abundance range of other elements like Ca, Sc, and Ni, confirms that Tuc~V is an ultra-faint dwarf (UFD) galaxy. The variation in abundances, highlighted by [Mg/Ca] ratios ranging from $+0.89$ to $-0.75$, among the stars, demonstrates that the chemical enrichment history of Tuc~V was very inhomogeneous. Tuc~V is only the second UFD galaxy in which stars located at large distances from the galactic center have been analyzed, along with Tucana~II. The chemical diversity seen in these two galaxies, driven by the composition of the non-central member stars, suggests that distant member stars are important to include when classifying faint satellites and that these systems may have experienced more complex chemical enrichment histories than previously anticipated., Comment: 19 pages, 11 figures, accepted for publication in ApJ

Binary Cepheids with giant companions are crucial for studying the physical properties of Cepheid variables, providing the best means to measure their masses. Systems composed of two Cepheids are even more important but to date, only one such system in the Large Magellanic Cloud (LMC) was known. Our current aim is to increase the number of these systems tenfold and provide their basic characteristics. The final goal is to obtain the physical properties of the component Cepheids, including their masses and radii, and to learn about their evolution in the multiple systems, also revealing their origin. We started a spectroscopic monitoring of nine unresolved pairs of Cepheids from the OGLE catalog, to check if they are gravitationally bound. Two of these so-called double Cepheids are located in the LMC, five in the Small Magellanic Cloud (SMC), and two in the Milky Way (MW). We report the spectroscopic detection of binarity of all 9 of these double Cepheids with orbital periods from 2 to 18 years. This increases the number of known binary double (BIND) Cepheids from 1 to 10 and triples the number of all confirmed double-lined binary (SB2) Cepheids. For five BIND Cepheids disentangled pulsational light curves of the components show anti-correlated phase shifts due to orbital motion. We show the first empirical evidence that typical period-luminosity relations (PLRs) are rather binary Cepheid PLRs that include the companion's light. The statistics of pulsation period ratios of BIND Cepheids do not agree with those expected for pairs of the same-age Cepheids. These ratios together with the mass ratios far from unity suggest merger-origin of at least one component for about half of the systems. The SMC and MW objects are the first found in SB2 systems composed of giants in their host galaxies. The Milky Way BIND Cepheids are also the closest such systems, being located at about 11 and 26 kpc., Comment: 13 pages, 7 figures, 4 tables, accepted for publication in Astronomy & Astrophysics

A mapping is made between fermion exchange and excluded volume in the quantum-classical isomorphism using polymer self-consistent field theory. Apart from exchange, quantum particles are known to be exactly representable in classical statistical mechanics as ring polymers, with contours that are parametrized by the inverse thermal energy, often called the imaginary time. Evidence in support of a previously used approximation for fermion exchange in ring polymer self-consistent field theory is given, specifically, that the use of all-contour interactions in the mean field picture instead of equal imaginary time interactions is justified based on the symmetry of ring polymers. It is also shown that the removal of forbidden thermal trajectories, both those that violate excluded volume directly and those that represent topologically inaccessible microstates, is equivalent to antisymmetric exchange. The electron density of the beryllium atom is calculated with ring polymer self-consistent field theory ignoring classical correlations, and very good agreement is found with Hartree-Fock theory which also neglects Coulomb correlations. The total binding energies agree to within less than 6%, which while still far from chemical accuracy, is remarkable given that the field theory equations are derived from first principles with zero free parameters. The discrepancy between self-consistent field theory and Hartree-Fock theory is attributed to classical Coulomb self-interactions which are included in Hartree-Fock theory but not in self-consistent field theory. A potential method to improve the agreement by more accurately representing electron-electron self-interactions in self-consistent field theory is discussed, as are the implications for quantum foundations of the quantum-classical mapping between fermion exchange and thermal trajectory excluded volume., Comment: 17 pages, 2 figures

To obtain the best resolution for any measurement there is an ever-present challenge to achieve maximal differentiation between signal and noise over as fine of sampling dimensions as possible. In diffraction science these issues are particularly pervasive when analyzing small crystals, systems with diffuse scattering, or other systems in which the signal of interest is extremely weak and incident flux and instrument time is limited. We here demonstrate that the tool of compressed sensing, which has successfully been applied to photography, facial recognition, and medical imaging, can be effectively applied to diffraction images to dramatically improve the signal-to-noise ratio (SNR) in a data-driven fashion without the need for additional measurements or modification of existing hardware. We outline a technique that leverages compressive sensing to bootstrap a single diffraction measurement into an effectively arbitrary number of virtual measurements, thereby providing a means of super-resolution imaging.

To assess how the presence of surfactant in lung airways alters the flow of mucus that leads to plug formation and airway closure, we investigate the effect of insoluble surfactant on the instability of a viscoplastic liquid coating the interior of a cylindrical tube. Evolution equations for the layer thickness using thin-film and long-wave approximations are derived that incorporate yield-stress effects and capillary and Marangoni forces. Using numerical simulations and asymptotic analysis of the thin-film system, we quantify how the presence of surfactant slows growth of the Rayleigh-Plateau instability, increases the size of initial perturbation required to trigger instability and decreases the final peak height of the layer. When the surfactant strength is large, the thin-film dynamics coincide with the dynamics of a surfactant-free layer but with time slowed by a factor of four and the capillary Bingham number, a parameter proportional to the yield stress, exactly doubled. By solving the long-wave equations numerically, we quantify how increasing surfactant strength can increase the critical layer thickness for plug formation to occur and delay plugging. The previously established effect of the yield stress in suppressing plug formation [Shemilt et al., J. Fluid Mech., 2022, vol. 944, A22] is shown to be amplified by introducing surfactant. We discuss the implications of these results for understanding the impact of surfactant deficiency and increased mucus yield stress in obstructive lung diseases., Comment: 35 pages, 11 figures

We report the development of GPT-4, a large-scale, multimodal model which can accept image and text inputs and produce text outputs. While less capable than humans in many real-world scenarios, GPT-4 exhibits human-level performance on various professional and academic benchmarks, including passing a simulated bar exam with a score around the top 10% of test takers. GPT-4 is a Transformer-based model pre-trained to predict the next token in a document. The post-training alignment process results in improved performance on measures of factuality and adherence to desired behavior. A core component of this project was developing infrastructure and optimization methods that behave predictably across a wide range of scales. This allowed us to accurately predict some aspects of GPT-4's performance based on models trained with no more than 1/1,000th the compute of GPT-4., Comment: 100 pages; updated authors list; fixed author names and added citation

The quantum-classical isomorphism for self-consistent field theory, which allows quantum particles in space-time to be represented as classical one-dimensional threads embedded in a five dimensional thermal-space-time, is summarized and used to explain a selection of quantum phenomena. Introduced by Feynman, and used for modern quantum simulations, the isomorphism, when phrased in a field-theoretic way, has been shown to be the same as quantum density functional theory, the theorems of which guarantee equivalent predictions with non-relativistic quantum mechanics. If the Feynman dimension is considered to be real, there is a duality between classical threads in five dimensions and quantum particles in four dimensions. Using the 5D picture, intuitive explanations are given for quantum phenomena including the uncertainty principle, tunnelling, geometric phase, and interference effects. Advantages of the 5D picture are presented, which include fewer postulates, no measurement problem, and the need for only classical concepts in the higher dimensional space. Limitations of the approach such as the interpretation of entanglement and spin are discussed., Comment: Submitted to International Journal of Theoretical Physics

We report the discovery of a surprising binary configuration of the double-mode Cepheid OGLE-LMC-CEP-1347 pulsating in the first (P_1=0.690d) and second overtone (P_2=0.556d) modes. The orbital period (P_orb=59d) of the system is five times shorter than the shortest known to date (310d) for a binary Cepheid. The Cepheid itself is also the shortest-period one ever found in a binary system and the first double-mode Cepheid in a spectroscopically double-lined binary. OGLE-LMC-CEP-1347 is most probably on its first crossing through the instability strip, as inferred from both its short period and fast period increase, consistent with evolutionary models, and from the short orbital period (not expected for binary Cepheids whose components have passed through the red giant phase). Our evolutionary analysis yielded a first-crossing Cepheid with a mass in a range of 2.9-3.4 Msun (lower than any measured Cepheid mass), consistent with observations. The companion is a stable star, at least two times fainter and less massive than the Cepheid (preliminary mass ratio q=0.55), while also redder and thus at the subgiant or more advanced evolutionary stage. To match these characteristics, the Cepheid has to be a product of binary interaction, most likely a merger of two less massive stars, which makes it the second known classical Cepheid of binary origin. Moreover, further evolution of the components may lead to another binary interaction., Comment: 6 pages, 4 figures, 1 table, published in The Astrophysical Journal Letters

Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modelled as Gaussian threads with ring-polymer architecture in a four dimensional thermal-space, and a Pauli potential is postulated based on classical excluded volume implemented in the thermal-space using Edwards/Flory-Huggins interactions in a mean-field approximation. Other approximations include a Fermi-Amaldi correction for electron-electron self-interactions, a spherical averaging approximation to reduce the dimensionality of the problem, and the neglect of correlations. Polymer scaling theory is used to show that the excluded volume form of Pauli potential reduces to the known Thomas-Fermi energy density in the uniform limit. Self-consistent equations are solved using a bilinear Fourier expansion, with radial basis functions, for the first eighteen elements of the periodic table. Radial electron densities show correct shell structure, and the errors on the total binding energies compared to known binding energies are less than 9% for the lightest elements and drop to 3% or less for atoms heavier than nitrogen. More generally, it is suggested that only two postulates are needed within classical statistical mechanics to achieve equivalency of predictions with static, non-relativistic quantum mechanics: First, quantum particles are modelled as Gaussian threads in four dimensional thermal-space and, second, pairs of threads (allowing for spin) are subject to classical excluded volume in the thermal-space. It is shown that these two postulates in thermal-space become the same as the Heisenberg uncertainty principle and the Pauli exclusion principle in three dimensional space., Comment: 23 pages, 3 figures, 1 table

Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is constructed directly from a Hamiltonian, so that the results are, in principle, valid at finite temperatures. The main governing equations are found to be a set of modified diffusion equations, and the set of self-consistent equations are essentially identical to those of a ring polymer system. The equations are shown to be equivalent to Kohn-Sham density functional theory, and to reduce to classical density functional theory, each under appropriate conditions. The obtained non-interacting kinetic energy functional is, in principle, exact, but suffers from the usual orbital-free approximation of the Pauli exclusion principle in additional to the exchange-correlation approximation. The equations are solved using the spectral method of polymer self-consistent field theory, which allows the set of modified diffusion equations to be evaluated for the same computational cost as solving a single diffusion equation. A simple exchange-correlation functional is chosen, together with a shell-structure-based Pauli potential, in order to compare the ensemble average electron densities of several isolated atom systems to known literature results. The agreement is excellent, justifying the alternative formalism and numerical method. Some speculation is provided on considering the time-like parameter in the diffusion equations, which is related to temperature, as having dimensional significance, and thus picturing point-like quantum particles instead as non-local, polymer-like, threads in a higher dimensional thermal-space. A consideration of the double-slit experiment from this point of view is speculated to provide results equivalent to the Copenhagen interpretation., Comment: 32 pages, 5 figures

Our goal is to determine, with high accuracy, the physical and orbital parameters of two double-lined eclipsing binary systems, where the components are two giant stars. We also aim to study the evolutionary status of the binaries, to derive the distances towards them by using a surface brightness-colour relation, and to compare these measurements with the measurements presented by the Gaia mission. In order to measure the physical and orbital parameters of the systems, we analysed the light curves and radial-velocity curves with the Wilson-Devinney code. We used V band and I-band photometry from the OGLE catalogue and near-infrared photometry obtained with the New Technology Telescope (NTT) equipped with the SOFI instrument. The spectroscopic data were collected with the HARPS spectrograph mounted at the ESO 3.6m telescope and the MIKE spectrograph mounted at the 6.5m Clay telescope. We present the first analysis of this kind for two evolved eclipsing binary systems from the OGLE catalogue: OGLE-BLG-ECL-305487 and OGLE-BLG-ECL-116218. The masses of the components of OGLE-BLG-ECL-305487 are $M_1$ = 1.059 $\pm$ 0.019 and $M_2$ = 0.991 $\pm$ 0.018 $M_\odot$, and the radii are $R_1$ = 19.27 $\pm$ 0.28 and $R_2$ = 29.99 $\pm$ 0.24 R$_\odot$. For OGLE-BLG-ECL-116218, the masses are $M_1$= 0.969 $\pm$ 0.012 and $M_2$= 0.983 $\pm$ 0.012 $M_\odot$, while the radii are $R_1$= 16.73 $\pm$ 0.28 and $R_2$= 22.06 $\pm$ 0.26 $R_\odot$. The evolutionary status of the systems is discussed based on the PARSEC and MIST isochrones. The ages of the systems were established to be between 7.3-10.9 Gyr for OGLE-BLG-ECL-305487 and around 10 Gyr for OGLE-BLG-ECL-116218. We also measured the distances to the binaries. For OGLE-BLG-ECL-305487, $d$= 7.80 $\pm$ 0.18 (stat.) $\pm$ 0.19 (syst.) kpc and for OGLE-BLG-ECL-116218, $d$= 7.57 $\pm$ 0.28 (stat.) $\pm$ 0.19 (syst.) kpc., Comment: 12 pages, 5 figures, accepted in A&A

We conduct hydrodynamical cosmological zoom simulations of fourteen voids to study the ability of haloes to accrete gas at different locations throughout the voids at z = 0. Measuring the relative velocity of haloes with respect to their ambient gas, we find that a tenth of the haloes are expected to be unable to accrete external gas due to its fast flow passed them (so called 'fast flow haloes'). These are typically located near void walls. We determine that these haloes have recently crossed the void wall and are still moving away from it. their motion counter to that of ambient gas falling towards the void wall results in fast flows that make external gas accretion very challenging, and often cause partial gas loss via the resultant ram pressures. Using an analytical approach, we model the impact of such ram pressures on the gas inside haloes of different masses. A halo's external gas accretion is typically cut off, with partial stripping of halo gas. For masses below a few times 10$^{9}$ M$_{\odot}$, their halo gas is heavily truncated but not completely stripped. We identify numerous examples of haloes with a clear jelly-fish like gas morphology, indicating their surrounding gas is being swept away, cutting them off from further external accretion. These results highlight how, even in the relatively low densities of void walls, a fraction of galaxies can interact with large-scale flows in a manner that has consequences for their gas content and ability to accrete gas., Comment: 13 pages, 8 figures

We describe the discovery of a solar neighborhood (d=468 pc) binary system with a main-sequence sunlike star and a massive non-interacting black hole candidate. The spectral energy distribution (SED) of the visible star is described by a single stellar model. We derive stellar parameters from a high signal-to-noise Magellan/MIKE spectrum, classifying the star as a main-sequence star with $T_{\rm eff} = 5972 \rm K$, $\log{g} = 4.54$, and $M = 0.91$ \msun. The spectrum shows no indication of a second luminous component. To determine the spectroscopic orbit of the binary, we measured radial velocities of this system with the Automated Planet Finder, Magellan, and Keck over four months. We show that the velocity data are consistent with the \textit{Gaia} astrometric orbit and provide independent evidence for a massive dark companion. From a combined fit of our spectroscopic data and the astrometry, we derive a companion mass of $11.39^{+1.51}_{-1.31}$\msun. We conclude that this binary system harbors a massive black hole on an eccentric $(e =0.46 \pm 0.02)$, $185.4 \pm 0.1$ d orbit. These conclusions are independent of \cite{ElBadry2022Disc}, who recently reported the discovery of the same system. A joint fit to all available data (including \cite{ElBadry2022Disc}'s) yields a comparable period solution, but a lower companion mass of $9.32^{+0.22}_{-0.21} M_{\odot}$. Radial velocity fits to all available data produce a unimodal solution for the period that is not possible with either data set alone. The combination of both data sets yields the most accurate orbit currently available., Comment: 30 pages, 17 figures, accepted to AAS journals (various changes in response to referee comments)

An alternative approach to density functional theory based on self-consistent field theory for ring polymers is applied to neutral atoms hydrogen to neon in their ground states. The spontaneous emergence of atomic shell structure and spherical symmetry-breaking of the total electron density is predicted by the model using ideas of polymer excluded-volume between pairs of electrons to enforce the Pauli-exclusion principle, and an exact electron self-interaction correction. The Pauli potential is approximated and correlations are neglected, leading to comparisons with Hartree-Fock theory, which also ignores correlations. The model shows excellent agreement with Hartree-Fock theory for the atomic binding energies and density profiles of the first six elements, providing exact matches for the elements hydrogen and helium. The predicted shell structure starts to deviate significantly past the element neon and spherical symmetry-breaking is first predicted to occur at carbon instead of boron. The self-consistent field theory energy functional which describes the model is decomposed into thermodynamic components to trace the origin of spherical symmetry-breaking. It is found to arise from the electron density approaching closer to the nucleus in non-spherical distributions, which lowers the energy despite resulting in frustration between the quantum kinetic energy, electron-electron interaction, and the Pauli exclusion interaction. The symmetry-breaking effect is also found to have minimal impact on the binding energies. The pair density profiles display behaviour similar to polymer macro-phase separation, where electron pairs occupy lobe-like structures that combined together, resemble traditional electronic orbitals. It is further shown that the predicted densities satisfy known constraints and produce the same total electronic density profile that is predicted by quantum mechanics., Comment: 29 pages, 7 figures, 5 tables

Dissolution of electrocatalysts during long-term and dynamic operation is a challenging problem in energy conversion and storage devices such as fuel cells and electrolyzers. To develop stable electrocatalysts, we adopt the design concept of segregation engineering, which uses solute segregation prone to electrochemical dissolution at internal defects, i.e., grain boundaries and dislocations. We showcase the feasibility of this approach by stabilizing a model Pt catalyst with an addition of more noble Au (approximately 5 atomic percent). We characterized the defects' nanoscale structure and chemistry, and monitored the electrochemical dissolution of Pt and PtAu alloys by online inductively coupled plasma mass spectrometry. Once segregated to defects, Au atoms can stabilize and hence passivate the most vulnerable sites against electrochemical dissolution and improve the stability and longevity of the Pt electrocatalysts by more than an order of magnitude. This opens pathways to use solute segregation to defects for the development of more stable nanoscale electrocatalysts, a concept applicable for a wide range of catalytic systems.

We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of a toxic protein in a specific region represented by a vertex. Over time, the accumulation of toxic proteins at vertices and their propagation along edges are modeled by a dynamical system on this graph. These dynamics provide an order on the edges of the graph according to the damage created by high concentrations of proteins. This sequence of edges defines a filtration of the graph. We consider different filtrations given by different disease seeding locations. To study this filtration we propose a new combinatorial and topological method. A filtration defines a maximal chain in the partially ordered set of spanning subgraphs ordered by inclusion. To identify similar graphs, and define a topological signature, we quotient this poset by graph homotopy equivalence, which gives maximal chains in a smaller poset. We provide an algorithm to compute this direct quotient without computing all subgraphs and then propose bounds on the total number of graphs up to homotopy equivalence. To compare the maximal chains generated by this method, we extend Kendall's $d_K$ metric for permutations to more general graded posets and establish bounds for this metric. We then demonstrate the utility of this framework on actual brain graphs by studying the dynamics of tau proteins on the structural connectome. {We show that the proposed topological brain chain equivalence classes distinguish different simulated subtypes of Alzheimer's disease., Comment: 33 pages, 13 figures, submitted to Journal of Applied and Computational Topology (APCT)

A representation of polymer self-consistent field theory equivalent to quantum density functional theory is given in terms of non-orthogonal basis sets. Molecular integrals and self-consistent equations for spherically symmetric systems using Gaussian basis functions are given, and the binding energies and radial electron densities of neutral atoms hydrogen through krypton are calculated. An exact electron self-interaction correction is adopted and the Pauli-exclusion principle is enforced through ideas of polymer excluded-volume. The atoms hydrogen through neon are additionally examined without some approximations which permit cancellation of errors. Correlations are neglected for both cases in the interest of simplicity and comparisons are made with Hartree-Fock theory. The implications of the Pauli-exclusion potential and its approximate form are discussed, and the Pauli model is analyzed using scaling theory for the uniform electron density case where the correct form of the Thomas-Fermi quantum kinetic energy and the Dirac exchange correction are recovered., Comment: 31 pages, 4 figures, 2 tables; submitted to Physical Chemistry Chemical Physics