A Combinatorial Algorithm to Establish a Fair Border

A finite algorithm is given for the following problem: a piece of land bordered by n countries is to be divided equally among these n countries in such a way that each country's share is connected and adjacent to its original border

Measured and predicted pressure distributions on the AFTI/F-111 mission adaptive wing

Flight tests have been conducted using an F-111 aircraft modified with a mission adaptive wing (MAW). The MAW has variable-camber leading and trailing edge surfaces that can change the wing camber in flight, while preserving smooth upper surface contours. This paper contains wing surface pressure measurements obtained during flight tests at Dryden Flight Research Facility of NASA Ames Research Center. Upper and lower surface steady pressure distributions were measured along four streamwise rows of static pressure orifices on the right wing for a leading-edge sweep angle of 26 deg. The airplane, wing, instrumentation, and test conditions are discussed. Steady pressure results are presented for selected wing camber deflections flown at subsonic Mach numbers up to 0.90 and an angle-of-attack range of 5 to 12 deg. The Reynolds number was 26 million, based on the mean aerodynamic chord. The MAW flight data are compared to MAW wind tunnel data, transonic aircraft technology (TACT) flight data, and predicted pressure distributions. The results provide a unique database for a smooth, variable-camber, advanced supercritical wing

Lucas' Theorem for Prime Powers

Lucas' theorem on binomial coefficients states that (AB)≡(arbr)⋯(a1b1)(a0b0)(mod p) where p is a prime and A = arpr + ⋯ + a0p + a0, B = brpr + ⋯ + b1p + b0 + are the p-adic expansions of A and B. If s ⩾ 2, it is shown that a similar formula holds modulo ps where the product involves a slightly modified binomial coefficient evaluated on blocks of s digits.

Flight test results from a supercritical mission adaptive wing with smooth variable camber

The mission adaptive wing (MAW) consisted of leading- and trailing-edge variable-camber surfaces that could be deflected in flight to provide a near-ideal wing camber shape for any flight condition. These surfaces featured smooth, flexible upper surfaces and fully enclosed lower surfaces, distinguishing them from conventional flaps that have discontinuous surfaces and exposed or semiexposed mechanisms. Camber shape was controlled by either a manual or automatic flight control system. The wing and aircraft were extensively instrumented to evaluate the local flow characteristics and the total aircraft performance. This paper discusses the interrelationships between the wing pressure, buffet, boundary-layer and flight deflection measurement system analyses and describes the flight maneuvers used to obtain the data. The results are for a wing sweep of 26 deg, a Mach number of 0.85, leading and trailing-edge cambers (delta(sub LE/TE)) of 0/2 and 5/10, and angles of attack from 3.0 deg to 14.0 deg. For the well-behaved flow of the delta(sub LE/TE) = 0/2 camber, a typical cruise camber shape, the local and global data are in good agreement with respect to the flow properties of the wing. For the delta(sub LE/TE) = 5/10 camber, a maneuvering camber shape, the local and global data have similar trends and conclusions, but not the clear-cut agreement observed for cruise camber

Active learning of the thermodynamics-dynamics tradeoff in protein condensates

Phase-separated biomolecular condensates exhibit a wide range of dynamical properties, which depend on the sequences of the constituent proteins and RNAs. However, it is unclear to what extent condensate dynamics can be tuned without also changing the thermodynamic properties that govern phase separation. Using coarse-grained simulations of intrinsically disordered proteins, we show that the dynamics and thermodynamics of homopolymer condensates are strongly correlated, with increased condensate stability being coincident with low mobilities and high viscosities. We then apply an "active learning" strategy to identify heteropolymer sequences that break this correlation. This data-driven approach and accompanying analysis reveal how heterogeneous amino-acid compositions and non-uniform sequence patterning map to a range of independently tunable dynamical and thermodynamic properties of biomolecular condensates

Front-loading Urban Stormwater Management for Success – A Perspective Incorporating Current Studies on the Implementation of Retrofit Low-impact Development

Recent work into the implementation of low-impact development (LID) suggests that a decentralized, source-control approach has the potential to significantly reduce urban stormwater runoff quantity. The practice of retrofit stormwater management is currently dominated by demonstration projects, and some additional momentum is required to spur adoption and upscaling of LID practices so that the scale of this management approach can better match the scale of disturbance. This momentum may be provided in part by targeted research into effectiveness of stormwater best management practices insofar as research accounts for cost and effectiveness (e.g., water quality benefits, and actual stormwater capture) under a variety of climate conditions. We posit that the factors of increasing public participation in stormwater management; engaging local agencies and non-governmental organizations (NGOs); application of proven source control methods to mitigate runoff formation; and science-based, comprehensive monitoring strategies are all important to the sustainable implementation of retrofit low-impact development. From the perspective of Federal researchers and local NGOs, this paper presents features, objectives, and costs of recent efforts to properly scale demonstration projects and broader LID initiatives. In order to realize the full benefits of decentralized LID stormwater management practices in urban and suburban areas, we conclude that a nexus must exist of a motivated and engaged citizenry, solid support from municipal and regional agencies, sound source control management practices, and follow-up monitoring to judge effectiveness

Globular Cluster Scale Sizes in Giant Galaxies: Orbital Anisotropy and Tidally Under-filling Clusters in M87, NGC 1399, and NGC 5128

We investigate the shallow increase in globular cluster half-light radii with projected galactocentric distance $R_{gc}$ observed in the giant galaxies M87, NGC 1399, and NGC 5128. To model the trend in each galaxy, we explore the effects of orbital anisotropy and tidally under-filling clusters. While a strong degeneracy exists between the two parameters, we use kinematic studies to help constrain the distance $R_\beta$ beyond which cluster orbits become anisotropic, as well as the distance $R_{f\alpha}$ beyond which clusters are tidally under-filling. For M87 we find $R_\beta > 27$ kpc and $20 < R_{f\alpha} 13$ kpc and $10 < R_{f\alpha} < 30$ kpc. The connection of $R_{f\alpha}$ with each galaxy's mass profile indicates the relationship between size and $R_{gc}$ may be imposed at formation, with only inner clusters being tidally affected. The best fitted models suggest the dynamical histories of brightest cluster galaxies yield similar present-day distributions of cluster properties. For NGC 5128, the central giant in a small galaxy group, we find $R_\beta > 5$ kpc and $R_{f\alpha} > 30$ kpc. While we cannot rule out a dependence on $R_{gc}$, NGC 5128 is well fitted by a tidally filling cluster population with an isotropic distribution of orbits, suggesting it may have formed via an initial fast accretion phase. Perturbations from the surrounding environment may also affect a galaxy's orbital anisotropy profile, as outer clusters in M87 and NGC 1399 have primarily radial orbits while outer NGC 5128 clusters remain isotropic.Comment: 16 pages, 7 figures, 4 tables, Accepted for publication in MNRA

Assessing the Affordability of Nutrient-Adequate Diets

The cost and affordability of least-cost healthy diets by time and place are increasingly used as a proxy for access to nutrient-adequate diets. Recent work has focused on the nutrient requirements of individuals, although most food and anti-poverty programs target whole households. This raises the question of how the cost of a nutrient-adequate diet can be measured for an entire household. This study identifies upper and lower bounds on the feasibility, cost, and affordability of meeting all household members' nutrient requirements using 2013-2017 survey data from Malawi. Findings show only a minority of households can afford the nutrient-adequate diet at either bound, with 20% of households able to afford the (upper bound) shared diets and 38% the individualized (lower bound) diets. Individualized diets are more frequently feasible with locally available foods (90% vs. 60% of the time) and exhibit more moderate seasonal fluctuation. To meet all members' needs, a shared diet requires a more nutrient-dense combination of foods that is more costly and exhibits more seasonality in diet cost than any one food group or the individualized diets. The findings further help adjudicate the extent to which nutritional behavioral change programs versus broader agricultural and food policies can be relied upon to improve individual access to healthy diets.Comment: 33 pages, 4 figure

Prebiotic Synthesis of Aspartate Using Life’s Metabolism as a Guide

A protometabolic approach to the origins of life assumes that the conserved biochemistry of metabolism has direct continuity with prebiotic chemistry. One of the most important amino acids in modern biology is aspartic acid, serving as a nodal metabolite for the synthesis of many other essential biomolecules. Aspartate’s prebiotic synthesis is complicated by the instability of its precursor, oxaloacetate. In this paper, we show that the use of the biologically relevant cofactor pyridoxamine, supported by metal ion catalysis, is sufficiently fast to offset oxaloacetate’s degradation. Cu2+-catalysed transamination of oxaloacetate by pyridoxamine achieves around a 5% yield within 1 h, and can operate across a broad range of pH, temperature, and pressure. In addition, the synthesis of the downstream product β-alanine may also take place in the same reaction system at very low yields, directly mimicking an archaeal synthesis route. Amino group transfer supported by pyridoxal is shown to take place from aspartate to alanine, but the reverse reaction (alanine to aspartate) shows a poor yield. Overall, our results show that the nodal metabolite aspartate and related amino acids can indeed be synthesised via protometabolic pathways that foreshadow modern metabolism in the presence of the simple cofactor pyridoxamine and metal ions