Voting rules can be assessed from quite different perspectives: the axiomatic, pragmatic, in terms of computational or conceptual simplicity, susceptibility to manipulation, and many others aspects. In this paper, we take machine learning perspective ask how prominent voting compare their learnability by a neural network. To address question, train network choosing Condorcet, Borda, plurality w...

The rank and invariants of a general lattice rule are conventionally deened in terms of the group-theoretic properties of the rule. Here we g i v e a constructive deenition of the rank and invariants using integer matrices. This underpins a nonabstract algorithm set in matrix algebra for obtaining the Sylow p-decomposition of a lattice rule. This approach is particularly useful when it is not k...

A mixing rule for the mixtures of hard-spheres is presented which can be reduced to the standard van der Waals mixing rule at low densities. The effectiveness of the mixing rule for the size and energy parameters of lennard-Jones fluid are examined by combining them with an equation of state to calculate thermodynamic properties. The results of calculation are compared with the molecular dy...

Evolutionary trends in body size have been identified within several lineages, but not all have followed Cope’s rule, which states that average body size within a taxon tends to increase over time. In organisms such as parasites, space constraints may have shaped the evolution of body sizes, favouring small-bodied taxa capable of exploiting new niches. Here, the average adult body sizes of fami...