The Difference ?-Calculus: A Language for Difference Categories

Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian differential category being satisfied only "up to an infinitesimal perturbation". In this work, we construct a simply-typed calculus in the spirit of the differential ?-calculus equipped with syntactic "infinitesimals" and show how its models correspond to difference ?-categories, a family of Cartesian difference categories equipped with suitably well-behaved exponentials

Phase-field modelling of the dynamics of Z-ring formation in liposomes: Onset of constriction and coarsening

We propose a model for the dynamics of the formation of rings of FtsZ on tubular liposomes which produce constriction on the corresponding membrane. Our phase-field model is based on a simple bending energy that captures the dynamics of the interplay between the protein and the membrane. The short-time regime is analyzed by a linear dispersion relation, with which we are able to predict the number of rings per unit length on a tubular liposome. We study numerically the long-time dynamics of the system in the non-linear regime where we observe coarsening of Z-rings on tubular liposomes. In particular, our numerical results show that, during the coarsening process, the number of Z-rings decreases as the radius of tubular liposome increases. This is consistent with the experimental observation that the separation between rings is proportional to the radius of the liposome. Our model predicts that the mechanism for the increased rate of coarsening in liposomes of larger radius is a consequence of the increased interface energy

Phase-field modelling of the dynamics of Z-ring formation in liposomes: Onset of constriction and coarsening

We propose a model for the dynamics of the formation of rings of FtsZ on tubular liposomes which produce constriction on the corresponding membrane. Our phase-field model is based on a simple bending energy that captures the dynamics of the interplay between the protein and the membrane. The short-time regime is analyzed by a linear dispersion relation, with which we are able to predict the number of rings per unit length on a tubular liposome. We study numerically the long-time dynamics of the system in the non-linear regime where we observe coarsening of Z-rings on tubular liposomes. In particular, our numerical results show that, during the coarsening process, the number of Z-rings decreases as the radius of tubular liposome increases. This is consistent with the experimental observation that the separation between rings is proportional to the radius of the liposome. Our model predicts that the mechanism for the increased rate of coarsening in liposomes of larger radius is a consequence of the increased interface energy

Fixing incremental computation: derivatives of fixpoints, and the recursive semantics of datalog

Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We generalise change structures to change actions, and study their algebraic properties. We develop change actions for common structures in computer science, including directed-complete partial orders and Boolean algebras. We then show how to compute derivatives of fixpoints. This allows us to perform incremental evaluation and maintenance of recursively defined functions with particular application generalised Datalog programs. Moreover, unlike previous results, our techniques are modular in that they are easy to apply both to variants of Datalog and to other programming languages

Shelf life of rabbit hamburgers ageing in vacuum or modified atmosphere packaging

Consumers demand high quality meat products with natural flavour and taste. The high quality and safety of fresh meat products are important features to be conserved during the storage and distribution. An approach to overcoming the short shelf-life problem of meat products is to use vacuum or modified atmosphere packaging. Rabbit hamburguers were made from loin and thigh meat; chilled hamburgers (0\ub0C\ub11; 5\ub0C\ub11), packed with vacuum (Multivax) or modified atmosphere (30%CO2-70%N2) were analysed at 1, 7, 14, 21 and 28 days after preparation (6 hamburgers/portion/packet/temperature/day). Lipid oxidation (Tbar\u2019s index), raw colour (CIELAB system, Minolta Chroma Meter-CR300) and pH (Testo 205) were determined. Fatty acids were analysed as methyl esters by gas chromatography. Cooking losses were determined by weight difference (grill, 71\ubaC\ub11\ubaC). Raw burgers were also analysed by an analytical panel of 8 trained assessors for overall colour, odour intensity and off-odours. Statistical analysis was performed using the Proc Mixed of SAS (2004) for repeated measurements. Differences between treatments were analysed by Tukey test (p<0.05). Vacuum and MAT packaging had similar effects on burgers quality until 28 days of storage. The longer time and higher temperature of conservation increased relative values of the colourimetric parameters, exudation and intensity of odour. Up to 28 days of storage, both lipid oxidation and the intensity of off-odour perception was very low. After 21 days, saturated and monounsaturated fatty acids and trombogenic index showed higher values while there was a lower content of polyunsaturated fatty acids. In conclusion, vacuum and MAT atmosphere packaging showed similar effects on the qualitative traits analysed which were influenced by the origin of meat, temperature of conservation and storage time