Abstract. The weighted transition polynomial of a multimatroid is a generalization of the Tutte polynomial. By defining the activity of a skew class with respect to a basis in a multimatroid, we obtain an activities expansion for the weighted transition polynomial. We also decompose the set of all transversals of a multimatroid as a union of subsets of transversals. Each term in the decomposition has the structure of a boolean lattice, and each transversal belongs to a number of terms depending only on the sizes of some of its skew classes. Further expressions for the transition polynomial of a multimatroid are obtained via an equivalence relation on its bases and by extending Kochol’s theory of compatible sets. We apply our multimatroid results to obtain a result of Morse about the transition polynomial of a delta-matroid and get a partition of the boolean lattice of subsets of elements of a delta-matroid determined by the feasible sets. Finally, we describe how multimatroids arise from graphs embedded in surfaces and apply our results to obtain an activities expansion for the topological transition polynomial. Our work extends results for the Tutte polynomial of a matroid.

The underlying reason for the local hyperthermia changes produced after a stimulus is not very well known and the relationship between local temperature changes and other physiological parameters has never been established. Current local temperature measurements are not completely accurate over time due to the physical constraints of the sensor, such as heat accumulation and dissipation. To clarify this issue, simultaneous in vivo measurements of local temperature, local blood-flow by laser Doppler flowmetry and neurotransmitter extracellular release using in vivo amperometry were performed with the aim of establishing their interrelationship. Local brain temperature measurements are usually obtained using thermocouples and thermistors, generally because of their small size and high level of accuracy. However, due to heat accumulation and dissipation effects on the sensor, the transient temperature measurement is not as accurate. In this paper, a simple method to obtain actual temperature fluctuations from measured values is proposed using classical digital signal processing techniques; the sensor was modeled via its transfer function. Deconvolution provides a method for obtaining actual temperature changes, enabling further comparative kinetic studies of all those physiological parameters, and helps to clarify the probable mechanism that underlies neurovascular coupling.