Geometry and Topology of Escape II: Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each endpoint of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an ``Epistrophe Start Rule'': a new epistrophe is spawned Delta = D+1 iterates after the segment to which it converges, where D is the minimum delay time of the complex.Comment: 13 pages, 8 figures, to appear in Chaos, second of two paper

Geometry and Topology of Escape I: Epistrophes

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an ``escape-time plot''. For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called ``epistrophes'', which occur at all levels of resolution within the escape-time plot. (The word ``epistrophe'' comes from rhetoric and means ``a repeated ending following a variable beginning''.) The epistrophes give the escape-time plot a certain self-similarity, called ``epistrophic'' self-similarity, which need not imply either strict or asymptotic self-similarity.Comment: 15 pages, 9 figures, to appear in Chaos, first of two paper

Using an unconventional climate record to link glacimarine sediments to turbidite frequencey in the

Master of ScienceGeologyUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/115441/1/39015074253363.pd

Examination of Winter Wheat Yield Response to Seed Source

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154489/1/pag2jpa19900551.pd

Integration of ancient DNA with transdisciplinary dataset finds strong support for Inca resettlement in the south Peruvian coast

Ancient DNA (aDNA) analysis provides a powerful means of investigating human migration, social organization, and a plethora of other crucial questions about humanity’s past. Recently, specialists have suggested that the ideal research design involving aDNA would include multiple independent lines of evidence. In this paper, we adopt a transdisciplinary approach integrating aDNA with archaeological, biogeochemical, and historical data to investigate six individuals found in two cemeteries that date to the Late Horizon (1400 to 1532 CE) and Colonial (1532 to 1825 CE) periods in the Chincha Valley of southern Peru. Genomic analyses indicate that these individuals are genetically most similar to ancient and present-day populations from the north Peruvian coast located several hundred kilometers away. These genomic data are consistent with 16th century written records as well as ceramic, textile, and isotopic data. These results provide some of the strongest evidence yet of state-sponsored resettlement in the pre-Colonial Andes. This study highlights the power of transdisciplinary research designs when using aDNA data and sets a methodological standard for investigating ancient mobility in complex societies

Geometry and Topology of Escape. II. Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each end point of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an “Epistrophe Start Rule:” a new epistrophe is spawned Δ=D+1 role= presentation style= display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ=D+1Δ=D+1 iterates after the segment to which it converges, where D role= presentation style= display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eD is the minimum delay time of the complex

The Double Disparity Facing Rural Local Health Departments

Residents of rural jurisdictions face significant health challenges, including some of the highest rates of risky health behaviors and worst health outcomes of any group in the country. Rural communities are served by smaller local health departments (LHDs) that are more understaffed and underfunded than their suburban and urban peers. As a result of history and current need, rural LHDs are more likely than their urban peers to be providers of direct health services, leading to relatively lower levels of population-focused activities. This review examines the double disparity faced by rural LHDs and their constituents: pervasively poorer health behaviors and outcomes and a historical lack of investment by local, state, and federal public health entities