Morse homology for the heat flow

We use the heat flow on the loop space of a closed Riemannian manifold to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined in the spirit of Floer theory by counting, modulo time shift, heat flow trajectories that converge asymptotically to nondegenerate closed geodesics of Morse index difference one.Comment: 89 pages, 3 figure

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broader efforts to support national production growth proved fiscally unsustainable, and once heavy subsidies were withdrawn, production fell (see table).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 Note on the Morse Index Theorem for Geodesics between Submanifolds in semi-Riemannian Geometry

The computation of the index of the Hessian of the action functional in semi-Riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint. Using this observation, we give an elementary proof of the Morse Index Theorem for Riemannian geodesics with two variable endpoints, in the spirit of the original Morse's proof. This approach reduces substantially the effort required in the proofs of the Theorem given in previous articles on the subject. Exactly the same argument works also in the case of timelike geodesics between two submanifolds of a Lorentzian manifold. For the extension to the lightlike Lorentzian case, just minor changes are required and one obtains easily a proof of the focal index theorems of Beem, Ehrlich and Kim.Comment: 12 pages, LaTeX2e, amsart style. To appear on the Journal of Mathematical Physic

Maize Revolutions in Sub-Saharan Africa

There have been numerous episodes of widespread adoption of improved seed and long-term achievements in the development of the maize seed industry in Sub-Saharan Africa. This summary takes a circumspect view of technical change in maize production. Adoption of improved seed has continued to rise gradually, now representing an estimated 44 percent of maize area in Eastern and Southern Africa (outside South Africa), and 60 percent of maize area in West and Central Africa. Use of fertilizer and restorative crop management practices remains relatively low and inefficient. An array of extension models has been tested and a combination of approaches will be needed to reach maize producers in heterogeneous agricultural environments. Yield growth overall has been 1 percent over the past half-century, although this figure masks the high variability in maize yields, as well as improvements in resistance to disease and abiotic pressures that would have caused yield decline in the absence of maize breeding progress. The authors argue that conducive policies are equally, if not more, important for maize productivity in the region than the development of new technology and techniques. Currently popular, voucher-based subsidies can “crowd out” the private sector and could be fiscally unsustainable.Sub-Saharan Africa, maize, seed, Agricultural and Food Policy, Production Economics,

A homoclinic tangle on the edge of shear turbulence

Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable manifolds separate the two in state space. In this Letter we describe a flow homoclinic to a time-periodic edge state. Its existence explains turbulent bursting through the classical Smale-Birkhoff theorem. During a burst, vortical structures and the associated energy dissipation are highly localized near the wall, in contrast to the familiar regeneration cycle

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

Turning on the heat: ecological response to simulated warming in the sea

Significant warming has been observed in every ocean, yet our ability to predict the consequences of oceanic warming on marine biodiversity remains poor. Experiments have been severely limited because, until now, it has not been possible to manipulate seawater temperature in a consistent manner across a range of marine habitats. We constructed a "hot-plate'' system to directly examine ecological responses to elevated seawater temperature in a subtidal marine system. The substratum available for colonisation and overlying seawater boundary layer were warmed for 36 days, which resulted in greater biomass of marine organisms and a doubling of space coverage by a dominant colonial ascidian. The "hot-plate'' system will facilitate complex manipulations of temperature and multiple stressors in the field to provide valuable information on the response of individuals, populations and communities to environmental change in any aquatic habitat

RXTE observations of the dipping low-mass X-ray binary 4U 1624-49

We analyse ~ 360 ks of archival data from the Rossi X-Ray Timing Explorer (RXTE) of the 21 hr orbital period dipping low-mass X-ray binary 4U 1624-49. We find that outside the dips the tracks in the colour-colour and hardness-intensity diagrams (CDs and HIDs) are reminiscent of those of atoll sources in the middle and upper parts of the banana branch. The tracks show secular shifts up to ~ 10%. We study the power spectrum of 4U 1624-49 as a function of the position in the CD. This is the first time power spectra of this source are presented. No quasi-periodic oscillations (QPOs) are found. The power spectra are dominated by very low frequency noise (VLFN), characteristic for atoll sources in the banana state, and band limited noise (BLN) which is not reliably detected but may, uncharacteristically, strengthen and increase in frequency with spectral hardness. The VLFN fits to a power law, which becomes steeper when the source moves to the harder part of the CD. We conclude that 4U 1624-49 is an atoll source which in our observations is in the upper banana branch. Combining this with the high (0.5-0.7 L_Edd) luminosity, the long-term flux stability of the source as seen with the RXTE All-Sky Monitor (ASM), and with the fact that it is an X-ray dip source, we conclude that 4U 1624-49 is most likely a GX atoll source such as GX 3+1 and GX 9+9, but seen edge on.Comment: 8 pages, 5 figures, 2 tables, accepted for publication in A&A. This version: a few typos correcte

Separation of complexity classes in Koiran's weak model

AbstractWe continue the study of complexity classes over the weak model introduced by P. Koiran. In particular we provide several separations of complexity classes, the most remarkable being the strict inclusion of P in NP. Other separations concern classes defined by weak polynomial time over parallel or alternating machines as well as over nondeterministic machines whose guesses are required to be 0 or 1

Can the initial singularity be detected by cosmological tests?

In the present paper we raise the question whether initial cosmological singularity can be proved from the cosmological tests. The classical general relativity predict the existence of singularity in the past if only some energy conditions are satisfied. On the other hand the latest quantum gravity applications to cosmology suggest of possibility of avoiding the singularity and replace it with the bounce. The distant type Ia supernovae data are used to constraints on bouncing evolutional scenario where square of the Hubble function $H^2$ is given by formulae $H^2=H^2_0[\Omega_{m,0}(1+z)^{m}-\Omega_{n,0}(1+z)^{n}]$, where $\Omega_{m,0}, \Omega_{n,0}>0$ are density parameters and $n>m>0$. We show that the on the base of the SNIa data standard bouncing models can be ruled out on the $4\sigma$ confidence level. If we add the cosmological constant to the standard bouncing model then we obtain as the best-fit that the parameter $\Omega_{n,0}$ is equal zero which means that the SNIa data do not support the bouncing term in the model. The bounce term is statistically insignificant the present epoch. We also demonstrate that BBN offer the possibility of obtaining stringent constraints of the extra term $\Omega_{n,0}$. The other observational test methods like CMB and the age of oldest objects in the Universe are used. We also use the Akaike informative criterion to select a model according to the goodness of fit and we conclude that this term should be ruled out by Occam's razor, which makes that the big bang is favored rather then bouncing scenario.Comment: 30 pages, 7 figures improved versio