Congruence lattices of semilattices

The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices of semilattices satisfies no nontrivial lattice identities. As a consequence it is shown that if V is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then all the members of V are groups with exponent dividing a fixed finite number

Satisfiability in multi-valued circuits

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates. We go outside Boolean realm and consider circuits built of any fixed set of gates on an arbitrary large finite domain. From the complexity point of view this is strictly connected with the problems of solving equations (or systems of equations) over finite algebras. The research reported in this work was motivated by a desire to know for which finite algebras $\mathbf A$ there is a polynomial time algorithm that decides if an equation over $\mathbf A$ has a solution. We are also looking for polynomial time algorithms that decide if two circuits over a finite algebra compute the same function. Although we have not managed to solve these problems in the most general setting we have obtained such a characterization for a very broad class of algebras from congruence modular varieties. This class includes most known and well-studied algebras such as groups, rings, modules (and their generalizations like quasigroups, loops, near-rings, nonassociative rings, Lie algebras), lattices (and their extensions like Boolean algebras, Heyting algebras or other algebras connected with multi-valued logics including MV-algebras). This paper seems to be the first systematic study of the computational complexity of satisfiability of non-Boolean circuits and solving equations over finite algebras. The characterization results provided by the paper is given in terms of nice structural properties of algebras for which the problems are solvable in polynomial time.Comment: 50 page

Maximal sublattices and Frattini sublattices of bounded lattices

We investigate the number and size of the maximal sublattices of a finite lattice. For any positive integer k, there is a finite lattice L with more that ]L]k sublattices. On the other hand, there are arbitrary large finite lattices which contain a maximal sublattice with only 14 elements. It is shown that every bounded lattice is isomorphic to the Frattini sublattice (the intersection of all maximal sublattices) of a finite bounded lattic

Physiological Correlates of Volunteering

We review research on physiological correlates of volunteering, a neglected but promising research field. Some of these correlates seem to be causal factors influencing volunteering. Volunteers tend to have better physical health, both self-reported and expert-assessed, better mental health, and perform better on cognitive tasks. Research thus far has rarely examined neurological, neurochemical, hormonal, and genetic correlates of volunteering to any significant extent, especially controlling for other factors as potential confounds. Evolutionary theory and behavioral genetic research suggest the importance of such physiological factors in humans. Basically, many aspects of social relationships and social activities have effects on health (e.g., Newman and Roberts 2013; Uchino 2004), as the widely used biopsychosocial (BPS) model suggests (Institute of Medicine 2001). Studies of formal volunteering (FV), charitable giving, and altruistic behavior suggest that physiological characteristics are related to volunteering, including specific genes (such as oxytocin receptor [OXTR] genes, Arginine vasopressin receptor [AVPR] genes, dopamine D4 receptor [DRD4] genes, and 5-HTTLPR). We recommend that future research on physiological factors be extended to non-Western populations, focusing specifically on volunteering, and differentiating between different forms and types of volunteering and civic participation