Algebraic methods for hybrid logics

Ph.D. (Mathematics)Algebraic methods have been largely ignored within the eld of hybrid logics. A main theme of this thesis is to illustrate the usefulness of algebraic methods in this eld. It is a well-known fact that certain properties of a logic correspond to properties of particular classes of algebras, and that we therefore can use these classes of algebras to answer questions about the logic. The rst aim of this thesis is to identify a class of algebras corresponding to hybrid logics. In particular, we introduce hybrid algebras as algebraic semantics for the better known hybrid languages in the literature. The second aim of this thesis is to use hybrid algebras to solve logical problems in the eld of hybrid logic. Specically, we will focus on proving general completeness results for some well-known hybrid logics with respect to hybrid algebras. Next, we study Sahlqvist theory for hybrid logics. We introduce syntactically de ned classes of hybrid formulas that have rst-order frame correspondents, which are preserved under taking Dedekind MacNeille completions of atomic hybrid algebras, and which are preserved under canonical extensions of permeated hybrid algebras. Finally, we investigate the nite model property (FMP) for several hybrid logics. In particular, we give analogues of Bull's theorem for the hybrid logics under consideration in this thesis. We also show that if certain syntactically de ned classes of hybrid formulas are added to the normal modal logic S4 as axioms, we obtain hybrid logics with the nite model property

A representation of odd Sugihara chains via weakening relations

We present a relational representation of odd Sugihara chains. The elements of the algebra are represented as weakening relations over a particular poset which consists of two densely embedded copies of the rationals. Our construction mimics that of Maddux (2010) where a relational representation of the even Sugihara chains is given. An order automorphism between the two copies of the rationals is the key to ensuring that the identity element of the monoid is fixed by the involution.Comment: 14 pages, 1 figur

Representable distributive quasi relation algebras

We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (2013). Our definition uses a construction that starts with a poset. The algebra is concretely constructed as the lattice of upsets of a partially ordered equivalence relation. The key to defining the three negation-like unary operations is to impose certain symmetry requirements on the partial order. Our definition of representable distributive quasi relation algebras is easily seen to be a generalisation of the definition of representable relations algebras by Jonsson and Tarski (1948). We give examples of representable DqRAs and give a necessary condition for an algebra to be finitely representable. We leave open the questions of whether every DqRA is representable, and also whether the class of representable DqRAs forms a variety. Moreover, our definition provides many other opportunities for investigations in the spirit of those carried out for representable relation algebras

Dysregulation of DAF-16/FOXO3A-mediated stress responses accelerates T oxidative DNA damage induced aging

DNA damage is presumed to be one type of stochastic macromolecular damage that contributes to aging, yet little is known about the precise mechanism by which DNA damage drives aging. Here, we attempt to address this gap in knowledge using DNA repair-deficient C. elegans and mice. ERCC1-XPF is a nuclear endonuclease required for genomic stability and loss of ERCC1 in humans and mice accelerates the incidence of age-related pathologies. Like mice, ercc-1 worms are UV sensitive, shorter lived, display premature functional decline and they accumulate spontaneous oxidative DNA lesions (cyclopurines) more rapidly than wild-type worms. We found that ercc-1 worms displayed early activation of DAF-16 relative to wild-type worms, which conferred resistance to multiple stressors and was important for maximal longevity of the mutant worms. However, DAF- 16 activity was not maintained over the lifespan of ercc-1 animals and this decline in DAF-16 activation cor- responded with a loss of stress resistance, a rise in oxidant levels and increased morbidity, all of which were cep- 1/ p53 dependent. A similar early activation of FOXO3A (the mammalian homolog of DAF-16), with increased resistance to oxidative stress, followed by a decline in FOXO3A activity and an increase in oxidant abundance was observed in Ercc1-/- primary mouse embryonic fibroblasts. Likewise, in vivo, ERCC1-deficient mice had transient activation of FOXO3A in early adulthood as did middle-aged wild-type mice, followed by a late life decline. The healthspan and mean lifespan of ERCC1 deficient mice was rescued by inactivation of p53. These data indicate that activation of DAF-16/FOXO3A is a highly conserved response to genotoxic stress that is important for suppressing consequent oxidative stress. Correspondingly, dysregulation of DAF-16/FOXO3A appears to underpin shortened healthspan and lifespan, rather than the increased DNA damage burden itself

Flow and nutrient dynamics in a subterranean estuary (Waquoit Bay, MA, USA) : field data and reactive transport modeling

Author Posting. © Elsevier B.V., 2008. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 72 (2008): 3398-3412, doi:10.1016/j.gca.2008.04.027.A two-dimensional (2D) reactive transport model is used to investigate the controls on nutrient (NO3-, NH4+, PO4) dynamics in a coastal aquifer. The model couples density dependent flow to a reaction network which includes oxic degradation of organic matter, denitrification, iron oxide reduction, nitrification, Fe2+ oxidation and sorption of PO4 onto iron oxides. Porewater measurements from a well transect at Waquoit Bay, MA, USA indicate the presence of a reducing plume with high Fe2+, NH4+, DOC (dissolved organic carbon) and PO4 concentrations overlying a more oxidizing NO3--rich plume. These two plumes travel nearly conservatively until they start to overlap in the intertidal coastal sediments prior to discharge into the bay. In this zone, the aeration of the surface beach sediments drives nitrification and allows the precipitation of iron oxide, which leads to the removal of PO4 through sorption. Model simulations suggest that removal of NO3- through denitrification is inhibited by the limited overlap between the two freshwater plumes, as well as by the refractory nature of terrestrial DOC. Submarine groundwater discharge is a significant source of NO3- to the bay.This research was funded by the Netherlands Organisation for Scientific Research (NWO) and WHOI Guest Student Program (C. Spiteri), the Royal Netherlands Academy of Arts and Sciences (KNAW) and the Netherlands Organization for Scientific Research (NWO VIDI-grant) (C.P. Slomp), the US National Science Foundation NSF-OCE0095384 and NSF-OCE0425061 (M.A. Charette) and the Georgia Sea Grant of the National Sea Grant College Program of the U.S. Department of Commerce’s National Oceanic and Atmospheric Administration under NOAA Grant #NA04OAR4170033 (C. Meile)

Spontaneous DNA damage to the nuclear genome promotes senescence,redox imbalance and aging

Accumulation of senescent cells over time contributes to aging and age-related diseases. However, what drives senescence in vivo is not clear. Here we used a genetic approach to determine if spontaneous nuclear DNA damage is sufficient to initiate senescence in mammals. Ercc1-/Δ mice with reduced expression of ERCC1-XPF endonuclease have impaired capacity to repair the nuclear genome. Ercc1-/Δ mice accumulated spontaneous, oxidative DNA damage more rapidly than wild-type (WT) mice. As a consequence, senescent cells accumulated more rapidly in Ercc1-/Δ mice compared to repair-competent animals. However, the levels of DNA damage and senescent cells in Ercc1-/Δ mice never exceeded that observed in old WT mice. Surprisingly, levels of reactive oxygen species (ROS) were increased in tissues of Ercc1-/Δ mice to an extent identical to naturally-aged WT mice. Increased enzymatic production of ROS and decreased antioxidants contributed to the elevation in oxidative stress in both Ercc1-/Δ and aged WT mice. Chronic treatment of Ercc1-/Δ mice with the mitochondrial-targeted radical scavenger XJB-5–131 attenuated oxidative DNA damage, senescence and age-related pathology. Our findings indicate that nuclear genotoxic stress arises, at least in part, due to mitochondrial-derived ROS, and this spontaneous DNA damage is sufficient to drive increased levels of ROS, cellular senescence, and the consequent age-related physiological decline

Spontaneous DNA damage to the nuclear genome promotes senescence, T redox imbalance and aging

Accumulation of senescent cells over time contributes to aging and age-related diseases. However, what drives senescence in vivo is not clear. Here we used a genetic approach to determine if spontaneous nuclear DNA damage is sufficient to initiate senescence in mammals. Ercc1-/Δ mice with reduced expression of ERCC1-XPF endonuclease have impaired capacity to repair the nuclear genome. Ercc1-/Δ mice accumulated spontaneous, oxidative DNA damage more rapidly than wild-type (WT) mice. As a consequence, senescent cells accumulated more rapidly in Ercc1-/Δ mice compared to repair-competent animals. However, the levels of DNA damage and senescent cells in Ercc1-/Δ mice never exceeded that observed in old WT mice. Surprisingly, levels of reactive oxygen species (ROS) were increased in tissues of Ercc1-/Δ mice to an extent identical to naturally-aged WT mice. Increased enzymatic production of ROS and decreased antioxidants contributed to the elevation in oxidative stress in both Ercc1-/Δ and aged WT mice. Chronic treatment of Ercc1-/Δ mice with the mitochondrial-targeted radical scavenger XJB-5–131 attenuated oxidative DNA damage, senescence and age-related pathology. Our findings indicate that nuclear genotoxic stress arises, at least in part, due to mitochondrial-derived ROS, and this spontaneous DNA damage is sufficient to drive increased levels of ROS, cellular senescence, and the consequent age-related physiological decline