Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Construction of equilibrium networks with an energy function

We construct equilibrium networks by introducing an energy function depending on the degree of each node as well as the product of neighboring degrees. With this topological energy function, networks constitute a canonical ensemble, which follows the Boltzmann distribution for given temperature. It is observed that the system undergoes a topological phase transition from a random network to a star or a fully-connected network as the temperature is lowered. Both mean-field analysis and numerical simulations reveal strong first-order phase transitions at temperatures which decrease logarithmically with the system size. Quantitative discrepancies of the simulation results from the mean-field prediction are discussed in view of the strong first-order nature.Comment: To appear in J. Phys.

Nonlinear preferential rewiring in fixed-size networks as a diffusion process

We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with exponents alpha and beta, the stationary states the degree distributions evolve towards exhibit a second order phase transition - from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at alpha = beta. Temporal evolution of the distribution in this critical regime is shown to follow a nonlinear diffusion equation, arriving at either pure or mixed power-laws, of exponents -alpha and 1-alpha

Effect of high hydrostatic pressure treatments on volatiles of berry purées

High hydrostatic pressure (HHP) technology, as a promising alternative of thermal-treatment and chemical preservatives, can be used to produce minimally processed foods. It has the advantage of affecting only non-covalent bonds of macromolecules in foods, and thus preserves nutritional components, taste, and flavour exceptionally well. However, HHP also influences enzymatic reactions of food. Although some of these changes are often beneficial, monitoring the potential effects of high pressure treatments — especially in the field of product and technology development — is essential. The aim of this study was to point out some parameters of high hydrostatic pressure technique (pressure, temperature, build-up time, holding time, number of cycles) that can substantially impact the sensory properties of treated products

Food security and sustainability - chances and limitations of agriculture

The increasing population of the world may induce various problems. There are two major fields; food security and adequate fresh water supply, which are predominant for all Global economic structures. On the other hand all activities implemented in favour of meeting the demand of the population, increase the ecological footprint and may risk sustainability of both mankind and its environment. The present study deals with an assessment of future trends on the basis of the present state of alimentation. Agriculture has a basic role in providing food for the human race. All sort of activities of that are in relation with the environment and at the same time they are driven by economic and social aspects. Sustainable agriculture can only be implemented if agricultural production can be run in an environment which is socially bearable, and economically viable. The scheme has to take into consideration that the society has to be equitable economically continuously. Whenever any of these interrelations cannot be manifested, the whole system may turn to be non-sustainable, or inefficient regarding food security

Food security and sustainability - chances and limitations of agriculture

The increasing population of the world may induce various problems. There are two major fields; food security and adequate fresh water supply, which are predominant for all Global economic structures. On the other hand all activities implemented in favour of meeting the demand of the population, increase the ecological footprint and may risk sustainability of both mankind and its environment. The present study deals with an assessment of future trends on the basis of the present state of alimentation. Agriculture has a basic role in providing food for the human race. All sort of activities of that are in relation with the environment and at the same time they are driven by economic and social aspects. Sustainable agriculture can only be implemented if agricultural production can be run in an environment which is socially bearable, and economically viable. The scheme has to take into consideration that the society has to be equitable economically continuously. Whenever any of these interrelations cannot be manifested, the whole system may turn to be non-sustainable, or inefficient regarding food security