Analysis of Basis Pursuit Via Capacity Sets

Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$ that allow its recovery using L1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of $D$ called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given $D$, called the "capacity sets". We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of $D\alpha=s$

Fodder legumes technology and farmer to farmer extension: a case of Desmodium and Calliandra in central Kenya

Adoption studies on fodders legume technologies have shown that spread of the technology is significantly enhanced by informal methods of dissemination especially farmer-to-farmer extension. It is not known which type of farmers are involved in this dissemination. The objective of this study was to identify farm and farmer characteristics that influence farmer-to farmer extension hence identify the type of farmers that can disseminate fodder legume technologies. A random sample of 130 farmers who had been given calliandra in central Kenya responded to a structured questionnaire. Information collected included farm and farmer characteristics and the number of farmers the original farmer had given Calliandra outside the original group. A tobit model was used to analyze the data to get the magnitude of the effects of factors affecting the probability and the intensity of giving out the fodder. Results showed that farmers with positions in farmer groups** , community responsibility**, larger amounts of desmodium on the their farms** , more years of the fodder on their farms***; low access to markets* and off farm income* , were positively involved in spread of the fodder legume. It was recommended that this type of farmers be targeted with support to increase spread of the technology

Factors influencing farmer-to-farmer extension of forage legume technology

Forage legumes have been introduced to farmers in Central Kenya between 1980 and 2002 through various Institutional and Projects’ efforts. The adoption rate of these forages among farmers has been found to be rather low, with the NDDP reporting only 1.9 % of farms surveyed and an ICRAF report indicating that the technology was only reaching 1 % of smallholder farms. An evaluation of adoption of Calliandra and Desmodium was conducted to identify farm characteristics affecting the likelihood of sharing of Desmodium and Calliandra technologies as well as to characterise the spread or diffusion of the technology from the original contact groups and the effect of distance from those groups. Three groups of farmers were approached. A first generation who received planting material from the distributors, a second generation who received planting materials from the former, and a randomly selected group of farmers at various distances from the first contacts. Informal discussions were held with the farmers and formal questionnaires filled. Out of the 133 first generation farmers contacted 64.7% still had Desmodium and 89.5% still had Calliandra. More farms in the contact sub-locations had the plants than the sub-locations further away. The small sample size of those with the forages could not allow effect of distance to be worked out. Tobit estimates of effects of farmer attributes influencing sharing of planting materials shows that the status of the household head in the community positively affected the likelihood of giving out planting material. The technology has a rather slow spread as indicated by percentages of farms with the forages. For better adoption and spread proponents of the technology should have the technology introduced to farmers who have substantial positions in farmer groups or have been bestowed community responsibility

Overshooting tipping point thresholds in a changing climate

Palaeorecords suggest that the climate system has tipping points, where small changes in forcing cause substantial and irreversible alteration to Earth system components called tipping elements. As atmospheric greenhouse gas concentrations continue to rise as a result of fossil fuel burning, human activity could also trigger tipping, and the impacts would be difficult to adapt to. Previous studies report low global warming thresholds above pre-industrial conditions for key tipping elements such as ice-sheet melt. If so, high contemporary rates of warming imply that exceeding these thresholds is almost inevitable, which is widely assumed to mean that we are now committed to suffering these tipping events. Here we show that this assumption may be flawed, especially for slow-onset tipping elements (such as the collapse of the Atlantic Meridional Overturning Circulation) in our rapidly changing climate. Recently developed theory indicates that a threshold may be temporarily exceeded without prompting a change of system state, if the overshoot time is short compared to the effective timescale of the tipping element. To demonstrate this, we consider transparently simple models of tipping elements with prescribed thresholds, driven by global warming trajectories that peak before returning to stabilize at a global warming level of 1.5 degrees Celsius above the pre-industrial level. These results highlight the importance of accounting for timescales when assessing risks associated with overshooting tipping point thresholds

Spacetime as a membrane in higher dimensions

By means of a simple model we investigate the possibility that spacetime is a membrane embedded in higher dimensions. We present cosmological solutions of d-dimensional Einstein-Maxwell theory which compactify to two dimensions. These solutions are analytically continued to obtain dual solutions in which a (d-2)-dimensional Einstein spacetime "membrane" is embedded in d-dimensions. The membrane solutions generalise Melvin's 4-dimensional flux tube solution. The flat membrane is shown to be classically stable. It is shown that there are zero mode solutions of the d-dimensional Dirac equation which are confined to a neighbourhood of the membrane and move within it like massless chiral (d-2)-dimensional fermions. An investigation of the spectrum of scalar perturbations shows that a well-defined mass gap between the zero modes and massive modes can be obtained if there is a positive cosmological term in (d-2) dimensions or a negative cosmological term in d dimensions.Comment: 30 pages, 4 figures in 10 files, epsf. This early brane world paper is being placed on the archive to make it more easily accessible, as its results are used in a new brane world construction in an accompanying submissio

Increases in the temperature seasonal cycle indicate long-term drying trends in Amazonia

Earth System Models project a wide range of rainfall changes in the Amazon rainforest, and hence changes in soil moisture and evapotranspiration. Hydrological changes are heterogeneous, meaning local measurements are too sparse to constrain projections of large-scale hydrological change. Here we show that changes in the amplitude of the temperature seasonal cycle are strongly correlated with annual mean evaporative fraction (surface latent heat flux as a fraction of surface net radiation) changes, across reanalyses and Earth System Model projections. We find an increase in annual temperature amplitude of 1 °C is associated with a reduction in evaporative fraction of up to 0.04. The observed temperature seasonal cycle amplitude increase (0.4 °C) over the last three decades implies Amazon drying, determined in the absence of soil or energy flux measurements, matches Earth System Model simulations of the recent past. Additionally, Earth System Models predict further temperature seasonal cycle amplitude increases, suggesting drying will continue with future climate change

Sedimentation record in the Konkan-Kerala Basin: implications for the evolution of the Western Ghats and the Western Indian passive margin

The Konkan and Kerala Basins constitute a major depocentre for sediment from the onshore hinterland of Western India and as such provide a valuable record of the timing and magnitude of Cenozoic denudation along the continental margin. This paper presents an analysis of sedimentation in the Konkan-Kerala Basin, coupledwith a mass balance study, and numerical modelling of flexural responses to onshore denudational unloading and o¡shore sediment loading in order to test competing conceptual models for the development of high-elevation passive margins. The Konkan-Kerala Basin contains an estimated 109,000 km<sup>3</sup>; of Cenozoic clastic sediment, a volume difficult to reconcile with the denudation of a downwarped rift flank onshore, and more consistent with denudation of an elevated rift flank. We infer from modelling of the isostatic response of the lithosphere to sediment loading offshore and denudation onshore that flexure is an important component in the development of the Western Indian Margin.There is evidence for two major pulses in sedimentation: an early phase in the Palaeocene, and a second beginning in the Pliocene. The Palaeocene increase in sedimentation can be interpreted in terms of a denudational response to the rifting between India and the Seychelles, whereas the mechanism responsible for the Pliocene pulse is more enigmatic

Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for publication in Phys. Rev.

Toward an internally consistent astronomical distance scale

Accurate astronomical distance determination is crucial for all fields in astrophysics, from Galactic to cosmological scales. Despite, or perhaps because of, significant efforts to determine accurate distances, using a wide range of methods, tracers, and techniques, an internally consistent astronomical distance framework has not yet been established. We review current efforts to homogenize the Local Group's distance framework, with particular emphasis on the potential of RR Lyrae stars as distance indicators, and attempt to extend this in an internally consistent manner to cosmological distances. Calibration based on Type Ia supernovae and distance determinations based on gravitational lensing represent particularly promising approaches. We provide a positive outlook to improvements to the status quo expected from future surveys, missions, and facilities. Astronomical distance determination has clearly reached maturity and near-consistency.Comment: Review article, 59 pages (4 figures); Space Science Reviews, in press (chapter 8 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age