A geometric study of Wasserstein spaces: Hadamard spaces

Optimal transport enables one to construct a metric on the set of (sufficiently small at infinity) probability measures on any (not too wild) metric space X, called its Wasserstein space W(X). In this paper we investigate the geometry of W(X) when X is a Hadamard space, by which we mean that $X$ has globally non-positive sectional curvature and is locally compact. Although it is known that -except in the case of the line- W(X) is not non-positively curved, our results show that W(X) have large-scale properties reminiscent of that of X. In particular we define a geodesic boundary for W(X) that enables us to prove a non-embeddablity result: if X has the visibility property, then the Euclidean plane does not admit any isometric embedding in W(X).Comment: This second version contains only the first part of the preceeding one. The visibility properties of W(X) and the isometric rigidity have been split off to other articles after a referee's commen

To sell or not to sell? Behavior of shareholders during price collapses

It is a common belief that the behavior of shareholders depends upon the direction of price fluctuations: if prices increase they buy, if prices decrease they sell. That belief, however, is more based on ``common sense'' than on facts. In this paper we present evidence for a specific class of shareholders which shows that the actual behavior of shareholders can be markedly different.Comment: 9 pages, 1 figure. To appear in International Journal of Modern Physics

Topologically Massive Gauge Theories and their Dual Factorised Gauge Invariant Formulation

There exists a well-known duality between the Maxwell-Chern-Simons theory and the self-dual massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the master theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.Comment: 1+7 pages, no figure

Yield gap and the shares of climate and crop management in yield and yield variability of staple crops in West Africa. [O-3330b-01]

" Yield gap " (Yg) is a key concept of agricultural science for identifying the room for improvement of yields through better management of the agroecosystem. in rainfed agriculture Yg is the difference between actual yield (Ya) and the theoretical water limited yield (Yw) that would be achieved if solar radiation, temperature and precipitations were the only factor limiting the crop's growth and yield. Changes in Yw over regions and years are due to climate-soil interactions that are not easily modified by crop management, whereas changes in Yg are due to limiting factors that are typically within the scope of crop management such as nutrient availability, weeds, and pests. We provide an example of yield gap estimates in semi-arid a frica, using yield and other agronomic data collected in famers' fields of Senegal in 1990 and 1991 and from 2006 to 2012. i t illustrates how contrarily to what most people would expect climate is not, on average, what most limits yields in that region: yet, actual yields are on average a quarter of water limited yield, and this is due to constraints whose reduction is technically possible albeit subject to the economic and environmental relevance of doing so. Most studies dealing with the impact of climate change on agriculture in West a frica compare Yw under present and future climate as predicted by climate models. t he magnitude of those predicted long term changes in Yw by 2050 is down to –20% in the worst scenario combining a +6°C change with a -20% rainfall change. s uch changes in water limited yields are certainly concerning, but they are remarkably small compared to the potential +390% increase that would result from closing the current yield gap. When considering yield variations observed across plots and years, and not anymore regional averages over a few years, what strikes is the stability of observed yields compared to variations of Yw. We used crop model simulations with historical series of 20 years of weather data to compare yield distributions over years of a crop grown using 3 contrasted levels of fertilisation and no incidence of weeds, pests or diseases. For each fertilisation level, the simulated yield reached a maximum value the 'best year' of the series. t he three fertilisation levels were chosen so that the maximum simulated yield reached 0.25 Yw, 0.5 Yw, and 0.75 Yw respectively. t he resulting simulated yield distributions show that even if management allows increasing the median yield, in many years the climate is the main limiting factor and fertilising has no or a slight impact only. i n other words, the way the current climate limits crop production in this region is by making uncertain the output of investing for high yields. Buying fertilizers or working hard for manure collection, transport and distribution do not translate, a certain number of years, into more production. For farmers struggling for the daily subsistence of their family, that kind of risk may not be justified while alternative use of family resources in cash and labour force provide less risky ways to produce subsistence means. Until recently, in many farming systems of West africa, the growth in food needs due to population growth in rural areas was matched thanks to increases in cultivated or pasted areas rather than increases in crop yields or livestock pressure on land (i.e extension rather than intensification of crop or livestock activities). When rural families reached the limits of this strategy, migrations of many kinds of distance and duration became the adjustment variable to the gap between resources available from farming and population needs. T his suggests that for many, it is less risky to leave home than to intensify cropping or livestock systems. Anyway, as job opportunities for migrants from the rural zones are currently low in West african cities and elsewhere, there are legitimate concerns about the way this strategy may soon reach its limit as well. i n terms of climate change, the worst scenario for farmers of that region would be if crop intensification became even more risky under future climate than at present. t here is thus an urgent need for joint agronomic and climate research to go beyond the prediction of Yw or of yield under unchanged crop management and determine whether or not the future climate will increase the yield risks associated with crop intensification in that region. But this should not divert from designing and implementing policies incentive to such intensification under present climate, as this might be much easier now than later. (Texte intégral

Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states

We examine the relation between different electronic transport phenomena in a Fabry-Perot interferometer in the fractional quantum Hall regime. In particular, we study the way these phenomena reflect the statistics of quantum Hall quasi-particles. For two series of states we examine, one abelian and one non-abelian, we show that the information that may be obtained from measurements of the lowest order interference pattern in an open Fabry-Perot interferometer is identical to the one that may be obtained from the temperature dependence of Coulomb blockade peaks in a closed interferometer. We argue that despite the similarity between the experimental signatures of the two series of states, interference and Coulomb blockade measurements are likely to be able to distinguish between abelian and non-abelian states, due to the sensitivity of the abelian states to local perturbations, to which the non-abelian states are insensitive.Comment: 10 pages. Published versio

Protocol dependence of the jamming transition

We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via purely repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to induce jamming in initially unjammed packings from the measured probability to jam at packing fraction $\phi$ from isotropic compression. We compare our predictions to results from numerical simulations of jamming and find quantitative agreement. We also show that the packing fraction range, over which strain-induced jamming occurs, tends to zero in the large system limit for frictionless packings with overdamped dynamics.Comment: 8 pages, 7 figure

Magnetoconductance oscillations in quasiballistic multimode nanowires

We calculate the conductance of quasi-one-dimensional nanowires with electronic states confined to a surface charge layer, in the presence of a uniform magnetic field. Two-terminal magnetoconductance (MC) between two leads deposited on the nanowire via tunnel barriers is dominated by density-of-states (DOS) singularities, when the leads are well apart. There is also a mesoscopic correction due to a higher-order coherent tunneling between the leads for small lead separation. The corresponding MC structure depends on the interference between electron propagation via different channels connecting the leads, which in the simplest case, for the magnetic field along the wire axis, can be crudely characterized by relative winding numbers of paths enclosing the magnetic flux. In general, the MC oscillations are aperiodic, due to the Zeeman splitting, field misalignment with the wire axis, and a finite extent of electron distribution across the wire cross section, and are affected by spin-orbit coupling. The quantum-interference MC traces contain a wealth of information about the electronic structure of multichannel wires, which would be complimentary to the DOS measurements. We propose a four-terminal configuration to enhance the relative contribution of the higher-order tunneling processes and apply our results to realistic InAs nanowires carrying several quantum channels in the surface charge-accumulation layer.Comment: 11 pages, 8 figure