The logic of equilibrium and abelian lattice ordered groups

We introduce a deductive system Bal which models the logic of balance of opposing forces or of balance between conflicting evidence or influences. ‘‘Truth values’’ are interpreted as deviations from a state of equilibrium, so in this sense, the theorems of Bal are to be interpreted as balanced statements, for which reason there is only one distinguished truth value, namely the one that represents equilibrium. The main results are that the system Bal is algebraizable in the sense of [5] and its equivalent algebraic semantics BAL is definitionally equivalent to the variety of abelian lattice ordered groups, that is, the categories of the algebras in BAL and of l–groups are isomorphic (see [10], Ch.4, 4). We also prove the deduction theorem for Bal and we study different kinds of semantic consequence associated to Bal. Finally, we prove the co-NP-completeness of the tautology problem of Bal.Departamento de Matemátic

On a Definition of a Variety of Monadic ℓ-Groups

In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor K∙, motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category MV∙ of monadic MV-algebras induced by “Kalman’s functor” K∙. Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor Γ♯, that is “parallel” to the well known functor Γ between ℓ and MV-algebras.Facultad de Ciencias Exacta

Transitions at CpG Dinucleotides, Geographic Clustering of TP53 Mutations and Food Availability Patterns in Colorectal Cancer

Colorectal cancer is mainly attributed to diet, but the role exerted by foods remains unclear because involved factors are extremely complex. Geography substantially impacts on foods. Correlations between international variation in colorectal cancer-associated mutation patterns and food availabilities could highlight the influence of foods on colorectal mutagenesis. mutations from 12 countries/geographic areas. For food availabilities, we relied on data extracted from the Food Balance Sheets of the Food and Agriculture Organization of the United Nations. Dendrograms for mutation sites, mutation types and food patterns were constructed through Ward's hierarchical clustering algorithm and their stability was assessed evaluating silhouette values. Feature selection used entropy-based measures for similarity between clusterings, combined with principal component analysis by exhaustive and heuristic approaches. hotspots. Pearson's correlation scores, computed between the principal components of the datamatrices for mutation types, food availability and mutation sites, demonstrated statistically significant correlations between transitions at CpGs and both mutation sites and availabilities of meat, milk, sweeteners and animal fats, the energy-dense foods at the basis of “Western” diets. This is best explainable by differential exposure to nitrosative DNA damage due to foods that promote metabolic stress and chronic inflammation

TOPOLOGICALLY INSEPARABLE FUNCTIONS II:

Abstract. Given a set A and a function f: A − → A, we study the set of all functions g: A − → A that are continuous for all topologies for which f continuous. We prove that in a sense to be made precise in the text, for any essentially infinitary function f, any non–constant such g equals f n, for some n ∈ N. We also prove a similar result for the clone of n –ary functions from A n − → A

Abstract. Given a set A and a function f: A

Given a set A and a function f : A A, we study the set of all functions g : A A that are continuous for all topologies for which f continuous. We prove that in a sense to be made precise in the text, for any essentially infinitary function f , any non--constant such g equals N . We also prove a similar result for the clone of n --ary functions from A A

Interpretability into Lukasiewicz Algebras

In this paper we give a characterization of all the interpretations of the varieties of bounded distributive lattices, De Morgan algebras and  Lukasiewicz algebras of order m in the variety of  Lukasiewicz algebras of order n. In the case of distributive lattices we give a structure theorem that is generalized to De Morgan algebras and to  Lukasiewicz algebras of order m. In the last two cases we also give the number of such interpretations.