Optimal Transportation Theory with Repulsive Costs

This paper intents to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions. We introduce some aspects of the Density Functional Theory (DFT) from a mathematical point of view, and revisit the theory of optimal transport from its perspective. Moreover, in the last three sections, we describe some recent and new theoretical and numerical results obtained for the Coulomb cost, the repulsive harmonic cost and the determinant cost.Comment: Survey for the special volume for RICAM (Special Semester on New Trends in Calculus of Variations

On the duality between p-Modulus and probability measures

Motivated by recent developments on calculus in metric measure spaces $(X,\mathsf d,\mathfrak m)$, we prove a general duality principle between Fuglede's notion of $p$-modulus for families of finite Borel measures in $(X,\mathsf d)$ and probability measures with barycenter in $L^q(X,\mathfrak m)$, with $q$ dual exponent of $p\in (1,\infty)$. We apply this general duality principle to study null sets for families of parametric and non-parametric curves in $X$. In the final part of the paper we provide a new proof, independent of optimal transportation, of the equivalence of notions of weak upper gradient based on $p$-Modulus (Koskela-MacManus '98, Shanmugalingam '00) and suitable probability measures in the space of curves (Ambrosio-Gigli-Savare '11)Comment: Minor corrections, typos fixe

Ecological Networks and Ecosystem Services in Urban Regions Implementation and Planning Practices

In recent decades, urban developments, agriculture and growth of grey infrastructures have affected urban landscapes. The rapid expansions of cities have increasingly caused loss of biodiversity, degradation and fragmentation of habitats. In this context, Ecological Network (EN) and more recently Ecosystem Services (ES) have been the subject of increasing attention among academics and in global and European policies. EN has represented a concept to consider and plan for preserving biodiversity and sustainable use of resources. EN also provides ES, for instance, recreational services (such as the access to green space, recreation, and educational resources) and supporting services (such as safeguarding biodiversity and protecting natural environment). The benefits provided by those two ES have been mostly emphasised in the research fields of regional and urban planning. In addition, several metropolitan regions and cities have defined objectives that EN is meant to pursue, as well as planning practices to adopt. However, there is a clear difficulty to effectively implement EN concept and adopt sustainable planning practices. Often ENs are not considered within built areas and where new developments are proposed. On the other hand, the introduction of the ES concept is still limited in land use planning. Comprehensive studies on how the concepts of EN and ES have been employed in urban regions are still very limited. This study aims to understand the implementation of EN and ES concept in land use planning and the current use of both concepts in planning practices

A disorder analysis of the Ising model

Lattice studies of monopole condensation in QCD are based on the construction of a disorder parameter, a creation operator of monopoles which is written in terms of the gauge fields. This procedure is expected to work for any system which presents duality. We check it on the Ising model in 2d, which is exactly solvable. The output is an amusing exercise in statistical mechanics.Comment: 14 pages, 3 figure

Occurrence of <i>Philometra lateolabracis</i> (Nematoda: Philometridae) in the gonads of marine perciform fishes in the Mediterranean region

Gravid females of the nematode Philometra lateolabracis (Yamaguti, 1935), a parasite of gonads of marine perciform fishes, were found in wild and cultured dusky grouper Epinephelus marginatus (Lowe) from waters near the Balear Islands (Spain, Mediterranean Sea) and Sicily (Italy, Thyrrenean Sea), and in the greater amberjack Seriola dumerili (Risso) in Croatia (south-eastern Adriatic Sea). In wild E. marginatus in Spain, the overall prevalence was 21% and the intensity of infection 1 nematode per fish. The nematodes are briefly described and illustrated. The species Sanguinofilaria jordanoi López-Neyra, 1951, described from the ovary of Epinephelus gigas Brünich from Morocco, is synonymized with P. lateolabracis. This is the first documented record of P. lateolabracis from fishes of the Mediterranean region and its finding in S. dumerili represents a new host record. The possible importance of this pathogenic parasite for cultures of marine perciform fishes in the region is stressed

Vanishing conductivity of quantum solitons in polyacetylene

Quantum solitons or polarons are supposed to play a crucial role in the electric conductivity of polyacetylene, in the intermediate doping regime. We present an exact fully quantized calculation of the quantum soliton conductivity in polyacetylene and show that it vanishes exactly. This is obtained by applying a general method of soliton quantization, based on order-disorder duality, to a Z(2)-symmetric complex extension of the TLM dimerization effective field theory. We show that, in this theory, polyacetylene solitons are sine-Gordon solitons in the phase of the complex field.Comment: To appear in J. Phys. A: Math. Theor., 15 page