Maize breeding in East and Southern Africa, 1900–2000

"During the first half of the 20th century, African farmers transformed maize from a minor imported foodcrop into the continent's principal staple food. In the second half of the century, newly independent governments launched support programs that greatly expanded smallholder production, leading to substantial production surges of 10 to 20 years in duration. Today, after widespread adoption by both commercial farmers and smallholders, farmers now plant 58 percent of all maize area in East and Southern Africa to new high-yielding varieties, which on average outyield traditional varieties by 40–50 percent even without fertilizer....Though these maize-breeding efforts were an undeniable technical success, broader efforts to support national production growth proved fiscally unsustainable, and once heavy subsidies were withdrawn, production fell (see table). This qualified success story reveals important lessons about both the strengths and pitfalls of past agricultural development efforts in Africa." From Text.

A statistical approach to persistent homology

Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying space. In this paper we take a statistical approach to this problem. We assume that the data is randomly sampled from an unknown probability distribution. We define two filtered complexes with which we can calculate the persistent homology of a probability distribution. Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.Comment: 30 pages, 2 figures, minor changes, to appear in Homology, Homotopy and Application

Quantum and classical echoes in scattering systems described by simple Smale horseshoes

We explore the quantum scattering of systems classically described by binary and other low order Smale horseshoes, in a stage of development where the stable island associated with the inner periodic orbit is large, but chaos around this island is well developed. For short incoming pulses we find periodic echoes modulating an exponential decay over many periods. The period is directly related to the development stage of the horseshoe. We exemplify our studies with a one-dimensional system periodically kicked in time and we mention possible experiments.Comment: 7 pages with 6 reduced quality figures! Please contact the authors ([email protected]) for an original good quality pre-prin

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

A CrC^{r} Closing Lemma for a Class of Symplectic Diffeomorphisms

We prove a $C^r$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $C^r$ symplectic diffeomorphism, $r =1, 2, ...,$, with two dimensional center and close to a product map, the set of all periodic points is dense

The Low-Mass X-ray Binary X1822-330 in the Globular Cluster NGC 6652: A Serendipitous ASCA Observation

The Low Mass X-ray Binary (LMXB) X1822-330 in NGC 6652 is one of 12 bright, or transient, X-ray sources to have been discovered in Globular Clusters. We report on a serendipitous ASCA observation of this Globular Cluster LMXB, during which a Type I burst was detected and the persistent, non-burst emission of the source was at its brightest level recorded to date. No orbital modulation was detected, which argues against a high inclination for the X1822-330 system. The spectrum of the persistent emission can be fit with a power law plus a partial covering absorber, although other models are not ruled out. Our time-resolved spectral analysis through the burst shows, for the first time, clear evidence for spectral cooling from kT=2.4+/-0.6 keV to kT=1.0+/0.1 keV during the decay. The measured peak flux during the burst is ~10% of the Eddington luminosity for a 1.4 Msun neutron star. These are characteristic of a Type I burst, in the context of the relatively low quiescent luminosity of X1822-330.Comment: 9 pages, 5 figures, accepted for Ap

Linking and causality in globally hyperbolic spacetimes

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in Lorentz manifolds. Let $M^m$ be a spacelike Cauchy surface in a globally hyperbolic spacetime $(X^{m+1}, g)$. The spherical cotangent bundle $ST^*M$ is identified with the space $N$ of all null geodesics in $(X,g).$ Hence the set of null geodesics passing through a point $x\in X$ gives an embedded $(m-1)$-sphere $S_x$ in $N=ST^*M$ called the sky of $x.$ Low observed that if the link $(S_x, S_y)$ is nontrivial, then $x,y\in X$ are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres $S_x$ are isotopic to fibers of $(ST^*M)^{2m-1}\to M^m.$ They are nonzero homologous and $lk(S_x,S_y)$ is undefined when $M$ is closed, while $alk(S_x, S_y)$ is well defined. Moreover, $alk(S_x, S_y)\in Z$ if $M$ is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If $(X,g)$ is such that $alk$ takes values in $\Z$ and $g$ is conformal to $g'$ having all the timelike sectional curvatures nonnegative, then $x, y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0$. We show that $x,y$ in nonrefocussing $(X, g)$ are causally unrelated iff $(S_x, S_y)$ can be deformed to a pair of $S^{m-1}$-fibers of $ST^*M\to M$ by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then $M$ is compact. We show that the universal cover of $M$ is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

Close proximity detection interference with acoustic telemetry: The importance of considering tag power output in low ambient noise environments

When employing acoustic telemetry to study aquatic species, understanding the functional dynamics of the monitoring system is essential for effective study design, data interpretation, and analysis. Typically, researchers are concerned with maximum effective detection range and consequently tend to employ the largest most powerful tags the study species can carry without considerable energetic burden. In ideal acoustic conditions of low ambient noise environments, low attenuation, and reflective structure, higher powered tags can be detected at larger distances from the receiver, but they can also be subject to the phenomenon ‘Close Proximity Detection Interference’ (CPDI). This occurs when reflective barriers, such as a calm water surface and/or hard substrate, result in strong transmission echoes that interfere with the transmission sequence. As a result, transmissions in close proximity to the receiver are not effectively decoded and logged

Observation of the Leggett-Rice effect in a unitary Fermi gas

We observe that the diffusive spin current in a strongly interacting degenerate Fermi gas of $^{40}$K precesses about the local magnetization. As predicted by Leggett and Rice, precession is observed both in the Ramsey phase of a spin-echo sequence, and in the nonlinearity of the magnetization decay. At unitarity, we measure a Leggett-Rice parameter $\gamma = 1.08(9)$ and a bare transverse spin diffusivity $D_0^\perp = 2.3(4)\,\hbar/m$ for a normal-state gas initialized with full polarization and at one fifth of the Fermi temperature, where $m$ is the atomic mass. One might expect $\gamma = 0$ at unitarity, where two-body scattering is purely dissipative. We observe $\gamma \rightarrow 0$ as temperature is increased towards the Fermi temperature, consistent with calculations that show the degenerate Fermi sea restores a non-zero $\gamma$. Tuning the scattering length $a$, we find that a sign change in $\gamma$ occurs in the range $0 < (k_F a)^{-1} \lesssim 1.3$, where $k_F$ is the Fermi momentum. We discuss how $\gamma$ reveals the effective interaction strength of the gas, such that the sign change in $\gamma$ indicates a switching of branch, between a repulsive and an attractive Fermi gas.Comment: 9 pages, 5 figures; Changed to the more conventional kF=(3 pi^2 n)^1/3, instead of the polarized definition we used in v