Optimal Transport with Coulomb cost. Approximation and duality

We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the approximating sequence to prove existence of maximizers for the dual problem (Kantorovich's potentials). Finally we observe that the same strategy can be applied to a more general class of costs and that a classical results on the topic cannot be applied here

The adoption of e-business technology by SMEs

The paper examines the key factors influencing the adoption ofe-business technology by SMEs. To this end, the paper draws on a rangeof literatures on the diffusion of new information and communicationtechnologies (ICTs), many of which have hitherto been treated asseparate. The reasons for this are two-fold. First, e-businesstechnologies are the latest in a line of new ICT technologies. Whenexploited successfully, ICTs have increased firm competitiveness eitherby raising the efficiency of internal communication and organisationand/or supply chain relationships, or by facilitating the development ofnew/improved products and services. Second, it is hypothesised that manyof the factors affecting the successful adoption of new technologies aregeneric in nature. With regards to SMEs specifically, consideration ofearlier research may assist us in identifying a set of enablers andbarriers to e-business adoption. Hence, by explicitly acknowledging thecontext and prior history of research in the area, we are able to mapout the dimensions of future theoretical and empirical research ine-business adoption by SMEs. In addition to drawing together factors identified by existing research,the paper highlights the implications of network externalities for thetiming of technology investments and the returns that accrue to earlyand late adopters. It also draws attention to a number of problemsassociated with the analytical concept of ‘the SME’ when it is appliedto this area. The research proceeds by clearly defining thetechnological and organisational characteristics of the e-business modeland a brief consideration of the trends in adoption in the UK vis-à-visadoption in the other G7 countries. Together these set up a detailedconsideration of the internal and external factors influencing adoption.A qualitative approach, in the form of a detailed case study, is thenused to explore the potential usefulness of the factors that have beenidentified. The results of these findings are then drawn together in theconcluding section of the paper.economics of technology ;

High temperature control in mediterranean greenhouse production: The constraints and the options

In the open field, the environment is a critical determinant of crop yield and produce quality and it affects the geographical distribution of most crop species. In contrast, in protected cultivation, environmental control allows the fulfillment of the actual needs depending on the technological level. The economic optimum, however, depends on the trade-off between the costs of increased greenhouse control and increase in return, dictated by yield quantity, yield quality and production timing. Additional constraints are increasingly applied for achieving environmental targets. However, the diverse facets of greenhouse technology in different areas of the world will necessarily require different approaches to achieve an improved utilization of the available resources. Although advanced technologies to improve resource use efficiency can be developed as a joint effort between different players involved in greenhouse technology, some specific requirements may clearly hinder the development of common “European” resource management models that, conversely should be calibrated for different environments. For instance, the quantification and control of resource fluxes can be better accomplished in a relatively closed and fully automated system, such as those utilized in the glasshouse of Northern-Central Europe, compared to Southern Europe, where different typologies of semi-open/semi-closed greenhouse systems generally co-exist. Based on these considerations, innovations aimed at improving resource use efficiency in greenhouse agriculture should implement these aspects and should reinforce and integrate information obtained from different research areas concerning the greenhouse production. Advancing knowledge on the physiology of high temperature adaptation, for instance, may support the development and validation of models for optimizing the greenhouse system and climate management in the Mediterranean. Overall, a successful approach will see horticulturists, plant physiologists, engineers and economists working together toward the definition of a sustainable greenhouse system

A study of the dual problem of the one-dimensional L-infinity optimal transport problem with applications

The Monge-Kantorovich problem for the infinite Wasserstein distance presents several peculiarities. Among them the lack of convexity and then of a direct duality. We study in dimension 1 the dual problem introduced by Barron, Bocea and Jensen. We construct a couple of Kantorovich potentials which is "as less trivial as possible". More precisely, we build a potential which is non constant around any point that the plan which is locally optimal moves at maximal distance. As an application, we show that the set of points which are displaced to maximal distance by a locally optimal transport plan is minimal

Duality theory and optimal transport for sand piles growing in a silos

We prove existence and uniqueness of solutions for a system of PDEs which describes the growth of a sandpile in a silos with flat bottom under the action of a vertical, measure source. The tools we use are a discrete approximation of the source and the duality theory for optimal transport (or Monge-Kantorovich) problems

Crop management in greenhouses: adapting the growth conditions to the plant needs or adapting the plant to the growth conditions?

Strategies for improving greenhouse crop production should target both developing advanced technological systems and designing improved plants. Based on greenhouse experiments, crop models and biotechnological tools, this paper will discuss the physiology of plant-greenhouse interactions. It is discussed how these interactions can be applied to control the production process at Northern and Mediterranean climatic conditions. Absorption of light by the leaves is important for maximum crop photosynthesis. For this, it is important to have plants that develop as fast as possible a sufficient leaf area index. The question is: what leaf area index is needed for optimal crop performance? Most of the light is absorbed by the upper part of the canopy. Can we improve the light distribution in the canopy and, moreover, does this increases yield or quality? Virtual plant models may help to address this question. In some cases removal of older leaves can improve yield, while in other cases removal of young leaves may accomplish the same objective. In summer time the light transmission of the greenhouse is often reduced by growers to avoid plant stress. However, in several cases this stress is only an indirect effect of light, because other growth factors (e.g. temperature, humidity) tend to be suboptimal. In Northern countries CO2 supply is commonly used. The introduction of semi-closed greenhouses allows to maintain high CO2 concentrations all year round. In Mediterranean countries, a large yield increase is still feasible by CO2 supply. Optimum growth conditions means that there is a good balance among different climate conditions. The source/sink ratio of a crop (ratio between production and demand of assimilates) often reflects whether these conditions are balanced. Variation in the source/sink balance affects formation and abortion of organs, product quality and production fluctuations. Some examples are shown on temperature control based on the source/sink balance of a crop. Drought and salinity may limit production especially in the Mediterranean. Morphological and metabolic traits, with known genetic bases, can be functionally altered to test current hypotheses on plant-environment interactions and eventually design a greenhouse plant. Reasonably, such a plant should have specific shoot vs. root developmental patterns, efficient water and nutrient uptake systems as well as other specific features that have not been sufficiently explored. Elucidation of the complex plant-greenhouse interactions would establish a physiological basis to improve both product quality and resource use efficiency in greenhous

The Monge problem with vanishing gradient penalization: Vortices and asymptotic profile

We investigate the approximation of the Monge problem (minimizing \int\_$\Omega$ |T (x) -- x| d$\mu$(x) among the vector-valued maps T with prescribed image measure T \# $\mu$) by adding a vanishing Dirichlet energy, namely $\epsilon$ \int\_$\Omega$ |DT |^2. We study the $\Gamma$-convergence as $\epsilon$ $\rightarrow$ 0, proving a density result for Sobolev (or Lipschitz) transport maps in the class of transport plans. In a certain two-dimensional framework that we analyze in details, when no optimal plan is induced by an H ^1 map, we study the selected limit map, which is a new "special" Monge transport, possibly different from the monotone one, and we find the precise asymptotics of the optimal cost depending on $\epsilon$, where the leading term is of order $\epsilon$| log $\epsilon$|

An incremental approach to the solution of global trajectory optimization problems

This paper presents an incremental approach to the solution of multiple gravity assist trajectories (MGA) with deep space maneuvers. The whole problem is decomposed in sub-problems that are solved incrementally. The solution of each sub-problem leads to a progressive reduction of the search space. Unlike other similar methods, the search for solutions of each sub-problem is performed through a stochastic approach. The resulting set of disconnected boxes is transformed into a connected collection of boxes through an affine transformation. For MGA problems, the incremental approach increases both the efficiency and reliability of the optimization process. Two relevant examples will illustrate the effectiveness of the proposed method

The \infty eigenvalue problem and a problem of optimal transportation

The so-called eigenvalues and eigenfunctions of the infinite Laplacian $\Delta_\infty$ are defined through an asymptotic study of that of the usual $p$-Laplacian $\Delta_p$, this brings to a characterization via a non-linear eigenvalue problem for a PDE satisfied in the viscosity sense. In this paper, we obtain an other characterization of the first eigenvalue via a problem of optimal transportation, and recover properties of the first eigenvalue and corresponding positive eigenfunctions

Factors affecting the adoption of intranets and extranets by SMEs: a UK study

The adoption of intranets and extranets involve major organisational innovation. Intranets alter the flows and content of internal communications, while extranets alter communications between the firm and its clients and suppliers. The paper identifies a number of potential factors that may affect adoption. These include internal and external business drivers, the role of the CEO/owner, firms’ absorptive capacity, firm size amongst SMEs, and business activity. Neither the relative size nor the business activities of SMEs have been considered in previous studies. Logit regressions are run on factors influencing the adoption of intranets and client extranet for a sample of 164 UK SMEs. The findings challenge two oft-stated views. First, that ICT adoption in SMEs depends on the CEO/owner being the ICT decision-maker. The findings clearly indicate that adoption is positively related to firm size. Larger sized SMEs firms have more complex organisational structures in which a specialist manager – typically holding the title ‘IT Manager’ – is the key decision-maker on ICT investments. Adoption depends on the quality and drive of these managers, not the CEO/owner. Second, the myth that services are technological laggards is clearly exposed. Knowledge intensive service firms, not manufacturing firms, are the champions of extranet technologies in this sample. In addition, both knowledge intensive service and manufacturing SMEs are key champions of intranet adoption. Expansion of national, not global, market share is the most important strategic objective identified in the study. The ability to integrate previously separate ICT systems is another important factor for intranet adopters. The results differ with respect to external customer and competitor pressure. These are found to be important in intranet adoption but not in extranet adoption. Only very weak support can be identified for the importance of absorptive capacity. A clear problem remains with regards to identifying a clear set of instruments with which to test for absorptive capacity.economics of technology ;