Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

Plant regeneration functional groups modulate the response to fire of soil enzyme activities in a Mediterranean shrubland

Soil enzymes are critical to soil nutrient cycling function but knowledge on the factors that control their response to major disturbances such as wildfires remains very limited. We evaluated the effect of fire-related plant functional traits (resprouting and seeding) on the resistance and resilience to fire of two soil enzyme activities involved in phosphorus and carbon cycling (acid phosphatase and β-glucosidase) in a Mediterranean shrublands in SE Spain. Using experimental fires, we compared four types of shrubland microsites: SS (vegetation patches dominated by seeder species), RR (patches dominated by resprouter species), SR (patches co-dominated by seeder and resprouter species), and IP (shrub interpatches). We assessed pre- and post-fire activities of the target soil enzymes, available P, soil organic C, and plant cover dynamics over three years after the fire. Post-fire regeneration functional groups (resprouter, seeder) modulated both pre- and post-fire activity of acid phosphatase and β-glucosidase, with higher activity in RR and SR patches than in SS patches and IP. However, we found no major differences in enzyme resistance and resilience between microsite types, except for a trend towards less resilience in SS patches. Fire similarly reduced the activity of both enzymes. However, acid phosphatase and β-glucosidase showed contrasting post-fire dynamics. While β-glucosidase proved to be rather resilient to fire, fully recovering three years after fire, acid phosphatase showed no signs of recovery in that period. Overall, the results indicate a positive influence of resprouter species on soil enzyme activity that is very resistant to fire. Long-lasting decrease in acid phosphatase activity probably resulted from the combined effect of P availability and post-fire drought. Our results provide insights on how plant functional traits modulate soil biochemical and microbiological response to fire in Mediterranean fire-prone shrublands.

Chemical diversity and potential biological functions of the pygidial gland secretions in two species of Neotropical dung roller beetles

Dung roller beetles of the genus Canthon (Coleoptera: Scarabaeinae) emit an odorous secretion from a pair of pygidial glands. To investigate the chemical composition of these secretions, we used stir bar sorptive extraction (SBSE), coupled with gas chromatography–mass spectrometry (GC–MS) for analysis of extracts of pygidial gland secretions secreted by the dung roller beetles Canthon femoralis femoralis and Canthon cyanellus cyanellus. Chemical analyses of volatiles collected from pygidial gland secretions comprise a great diversity of the functional groups. Chemical profile comparisons showed high intra- and interspecific variability. The pygidial gland secretion of Canthon f. femoralis was dominated by sesquiterpene hydrocarbons, whereas the profile of Canthon c. cyanellus was dominated by carboxylic acids. The different pygidial secretions have a high diversity of chemical compounds suggesting a multifunctional nature involving some key functions in the biology. We discuss the biological potential of these compounds found in the pygidial glands of each species with respect to their ecological and behavioral relevance.

On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.