Making a Sustainable Diet Acceptable: An Emerging Programming Model With Applications to Schools and Nursing Homes Menus

Background: Food consumption is one of the most important drivers of the relation between human well-being and Earth's ecosystems. The current production level is difficult to sustain without compromising environmental integrity or public health. This calls for a decisive change in food consumption patterns in order to improve nutrition quality while respecting biodiversity and ecosystems. This change will produce some effect only if it is also culturally acceptable, accessible, economically fair and affordable. The design of food plans is traditionally carried out using mathematical optimization models, such as linear programming. This method has proved to be successful in providing nutritionally adequate diets while minimizing their economic and environmental impact. Nevertheless, cultural habits as well as attractiveness and variety of meals is very difficult to deal with, and no fully satisfactory way to include these issues in linear programming has been found. Objective: The aim of this paper is to move from traditional linear programming to a new programming methodology in order to cope also with acceptability in the design of meal plans. Method: Binary integer linear programming is the new modeling paradigm. In the proposed model, meal plans consist of providing the sequence and composition of daily meals over a given period of time and each meal can be composed using dishes from a given set. Therefore, instead of defining just a level of consumption of food groups or food items, the proposed model provides a realistic menu. To cope with sustainability, the energy and nutritional content of each dish is calculated together with its price and environmental impact. Furthermore, acceptability can be explicitly taken into account in a very natural way, that is bounding the daily, weekly, or total repetitions of single dishes and of dishes in the same food groups. Results: The paper reviews three successful studies with increasing complexity considering lunch plans for schools and full-board menus for nursing homes. The case studies show a great reduction of the environmental impact of the meal plans while ensuring an adequate nutritional intake, affordable prices and most importantly the plans are varied and culturally acceptable

Small x Behavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep Inelastic Scattering Cross Section

We fit the reduced cross section for deep-inelastic electron scattering data to a three parameter ln^2 s fit, A + beta ln^2 (s/s_0), where s= [Q^2/x] (1-x) + m^2, and Q^2 is the virtuality of the exchanged photon. Over a wide range in Q^2 (0.11 < Q^2 < 1200 GeV^2) all of the fits satisfy the logarithmic energy dependence of the Froissart bound. We can use these results to extrapolate to very large energies and hence to very small values of Bjorken x -- well beyond the range accessible experimentally. As Q^2 --> infinity, the structure function F_2^p(x, Q^2) exhibits Bjorken scaling, within experimental errors. We obtain new constraints on the behavior of quark and antiquark distribution functions at small x.Comment: 10 pages, 2 figure

On the pulsating strings in AdS_5 x T^{1,1}

We study the class of pulsating strings in AdS_5 x T^{1,1}. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we semiclassically quantize the theory and obtain the first correction to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators in the dual N=1 superconformal gauge field theory.Comment: 12 pages, improvements made, references adde

A Test of the AdS/CFT Correspondence Using High-Spin Operators

In two remarkable recent papers, hep-th/0610248 and hep-th/0610251, the complete planar perturbative expansion was proposed for the universal function of the coupling, f(g), appearing in the dimensions of high-spin operators of the N=4 SYM theory. We study numerically the integral equation derived in hep-th/0610251, which implements a resummation of the perturbative expansion, and find a smooth function that approaches the asymptotic form predicted by string theory. In fact, the two leading terms at strong coupling match with high accuracy the results obtained for the semiclassical folded string spinning in $AdS_5$. This constitutes a remarkable confirmation of the AdS/CFT correspondence for high-spin operators, and equivalently for the cusp anomaly of a Wilson loop. We also make a numerical prediction for the third term in the strong coupling series.Comment: 11 pages, 1 figure; added references, corrected typo

Knowledge, Food and Place: a way of producing a way of knowing

The article examines the dynamics of knowledge in the valorisation of local food, drawing on the results from the CORASON project (A cognitive approach to rural sustainable development: the dynamics of expert and lay knowledge), funded by the EU under its Framework Programme 6. It is based on the analysis of several in-depth case studies on food relocalisation carried out in 10 European countries

A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

Implications of Hadron Collider Observables on Parton Distribution Function Uncertainties

Standard parton distribution function sets do not have rigorously quantified uncertainties. In recent years it has become apparent that these uncertainties play an important role in the interpretation of hadron collider data. In this paper, using the framework of statistical inference, we illustrate a technique that can be used to efficiently propagate the uncertainties to new observables, assess the compatibility of new data with an initial fit, and, in case the compatibility is good, include the new data in the fit.Comment: 22 pages, 5 figure

Baryonic Generating Functions

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.Comment: 44 pages, 7 figures; fonts change