A Holocene paleoenvironmental record based on ungulate stable isotopes from Lukenya Hill, Kenya

Investigating the development of Holocene behavioral adaptations requires knowing how and why different human groups are distributed on the landscape. An expanded dataset of site-specific environmental and habitat reconstructions from eastern Africa are crucial contextual components necessary for pushing this line of inquiry forward. This paper provides localized paleoenvironmental data from Holocene deposits at the multi-site Lukenya Hill archaeological complex on the Athi-Kapiti Plains of Kenya. Lukenya Hill preserves two temporal units, an early-mid Holocene (~9.0–4.6 ka) and a late Holocene (~2.3–1.2 ka), which span the end of the African Humid Period and the onset of late Holocene aridification. Carbon isotope analysis of herbivore tooth enamel (n = 22) indicates an increase in open grasslands over time with the early-mid Holocene having a woodier signal than the late Holocene and Recent populations in the Athi ecosystem. This pattern deviates from local environmental sequences in the Lake Victoria and Lake Turkana basins, providing additional evidence of heterogeneous habitat conditions during the Holocene of eastern Africa. The expansion of locally specific paleoecological datasets in eastern Africa allows for an examination of the role climate and ecology played in human economic and behavioral development during the Holocene.Accepted manuscrip

Counting fixed points and rooted closed walks of the singular map x↦xxnx \mapsto x^{x^n} modulo powers of a prime

The "self-power" map $x \mapsto x^x$ modulo $m$ and its generalized form $x \mapsto x^{x^n}$ modulo $m$ are of considerable interest for both theoretical reasons and for potential applications to cryptography. In this paper, we use $p$-adic methods, primarily $p$-adic interpolation, Hensel's lemma, and lifting singular points modulo $p$, to count fixed points and rooted closed walks of equations related to these maps when $m$ is a prime power. In particular, we introduce a new technique for lifting singular solutions of several congruences in several unknowns using the left kernel of the Jacobian matrix.Comment: 18 pages. Version 2 shortens proofs, reduces redundancy, and introduces new technique for counting rooted closed walks. Version 3 updates title to agree with journal publicatio

Morphometric approach to many-body correlations in hard spheres

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the \textit{morphometric} calculation of $n$-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where five-fold symmetric structures appear lower in free energy than four-fold symmetric structures, and from a single reaction path predict a relaxation barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.Comment: 6+17 pages, 3 figure

Counting Fixed Points, Two-Cycles, and Collisions of the Discrete Exponential Function using p-adic Methods

Brizolis asked for which primes p greater than 3 does there exist a pair (g, h) such that h is a fixed point of the discrete exponential map with base g, or equivalently h is a fixed point of the discrete logarithm with base g. Zhang (1995) and Cobeli and Zaharescu (1999) answered with a "yes" for sufficiently large primes and gave estimates for the number of such pairs when g and h are primitive roots modulo p. In 2000, Campbell showed that the answer to Brizolis was "yes" for all primes. The first author has extended this question to questions about counting fixed points, two-cycles, and collisions of the discrete exponential map. In this paper, we use p-adic methods, primarily Hensel's lemma and p-adic interpolation, to count fixed points, two cycles, collisions, and solutions to related equations modulo powers of a prime p.Comment: 14 pages, no figure

Matthewson St. United Methodist Church: Rehabilitation Feasiblity Report

The first-story floor plan was altered significantly during the 1951 renovations, and the entry vestibule is adorned with Neo-Gothic panelling. The chapel on the first floor is handsomely finished. The two-story sanctuary space has a semi-circular configuration with pews radiating from the altar, a balcony and substantial crown moulding

Is the Pale Blue Dot unique? Optimized photometric bands for identifying Earth-like exoplanets

The next generation of ground and space-based telescopes will image habitable planets around nearby stars. A growing literature describes how to characterize such planets with spectroscopy, but less consideration has been given to the usefulness of planet colors. Here, we investigate whether potentially Earth-like exoplanets could be identified using UV-visible-to-NIR wavelength broadband photometry (350-1000 nm). Specifically, we calculate optimal photometric bins for identifying an exo-Earth and distinguishing it from uninhabitable planets including both Solar System objects and model exoplanets. The color of some hypothetical exoplanets - particularly icy terrestrial worlds with thick atmospheres - is similar to Earth's because of Rayleigh scattering in the blue region of the spectrum. Nevertheless, subtle features in Earth's reflectance spectrum appear to be unique. In particular, Earth's reflectance spectrum has a 'U-shape' unlike all our hypothetical, uninhabitable planets. This shape is partly biogenic because O2-rich, oxidizing air is transparent to sunlight, allowing prominent Rayleigh scattering, while ozone absorbs visible light, creating the bottom of the 'U'. Whether such uniqueness has practical utility depends on observational noise. If observations are photon limited or dominated by astrophysical sources (zodiacal light or imperfect starlight suppression), then the use of broadband visible wavelength photometry to identify Earth twins has little practical advantage over obtaining detailed spectra. However, if observations are dominated by dark current then optimized photometry could greatly assist preliminary characterization. We also calculate the optimal photometric bins for identifying extrasolar Archean Earths, and find that the Archean Earth is more difficult to unambiguously identify than a modern Earth twin.Comment: 10 figures, 38 page