Bounded Arithmetic in Free Logic

One of the central open questions in bounded arithmetic is whether Buss' hierarchy of theories of bounded arithmetic collapses or not. In this paper, we reformulate Buss' theories using free logic and conjecture that such theories are easier to handle. To show this, we first prove that Buss' theories prove consistencies of induction-free fragments of our theories whose formulae have bounded complexity. Next, we prove that although our theories are based on an apparently weaker logic, we can interpret theories in Buss' hierarchy by our theories using a simple translation. Finally, we investigate finitistic G\"odel sentences in our systems in the hope of proving that a theory in a lower level of Buss' hierarchy cannot prove consistency of induction-free fragments of our theories whose formulae have higher complexity

Soluble tau species, not neurofibrillary aggregates, disrupt neural system integration in a tau transgenic model

Neurofibrillary tangles are a feature of Alzheimer disease and other tauopathies, and while they are generally believed to be markers of neuronal pathology, there is little evidence evaluating whether tangles directly impact neuronal function. To investigate the response of cells in hippocampal circuits to complex behavioral stimuli, we used an environmental enrichment paradigm to induce expression of an immediate-early gene, Arc, in the rTg4510 mouse model of tauopathy. These mice reversibly overexpress P301L tau and exhibit substantial neurofibrillary tangle deposition, neuronal loss, and memory deficits. Employing fluorescent in situ hybridization to detect Arc mRNA, we found that rTg4510 mice have impaired hippocampal Arc expression both without stimulation and in response to environmental enrichment; this likely reflects the combination of functional impairments of existing neurons and loss of neurons. However, tangle-bearing cells were at least as likely as non-tangle-bearing neurons to exhibit Arc expression in response to enrichment. Transgene suppression with doxycycline for 6 weeks resulted in increased percentages of Arc-positive cells in rTg4510 brains compared to untreated transgenics, restoring enrichment-induced Arc mRNA levels to that of wild-type controls despite the continued presence of neurofibrillary pathology. We interpret these data to indicate that soluble tau contributes to impairment of hippocampal function, while tangles do not preclude neurons from responding in a functional circuit

Inhibition of GSK3 abolishes bacterial-induced periodontal bone loss in mice

The tissue destruction that characterizes periodontitis is driven by the host response to bacterial pathogens. Inhibition of glycogen synthase kinase 3β (GSK3β) in innate cells leads to suppression of Toll-like receptor (TLR)-initiated proinflammatory cytokines under nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) p65 transcriptional control and promotion of cyclic adenosine monophosphate response element-binding (CREB)-dependent gene activation. Therefore, we hypothesized that the cell permeable GSK3-specific inhibitor, SB216763, would protect against alveolar bone loss induced by the key periodontal pathogen, Porphyromonas gingivalis (P. gingivalis), in a murine model. B6129SF2/J mice either were infected orally with P. gingivalis ATCC 33277; or treated with SB216763 and infected with P. gingivalis; sham infected; or exposed to vehicle only (dimethyl sulfoxide [DMSO]); or to GSK3 inhibitor only (SB216763). Alveolar bone loss and local (neutrophil infiltration and interleukin [IL]-17) and systemic (tumor necrosis factor [TNF], IL-6, Il-1β and IL-12/IL-23 p40) inflammatory indices also were monitored. SB216763 unequivocally abrogated mean P. gingivalis–induced bone resorption, measured at 14 predetermined points on the molars of defleshed maxillae as the distance from the cementoenamel junction to the alveolar bone crest (p < 0.05). The systemic cytokine response, the local neutrophil infiltration and the IL-17 expression were suppressed (p < 0.001). These data confirm the relevance of prior in vitro phenomena and establish GSK3 as a novel, efficacious therapeutic preventing periodontal disease progression in a susceptible host. These findings also may have relevance to other chronic inflammatory diseases and the systemic sequelae associated with periodontal infections

On the origin of interface states at oxide/III-nitride heterojunction interfaces

The energy spectrum of interface state density, D-it(E), was determined at oxide/III-N heterojunction interfaces in the entire band gap, using two complementary photo-electric methods: (i) photo-assisted capacitance-voltage technique for the states distributed near the midgap and the conduction band (CB) and (ii) light intensity dependent photo-capacitance method for the states close to the valence band (VB). In addition, the Auger electron spectroscopy profiling was applied for the characterization of chemical composition of the interface region with the emphasis on carbon impurities, which can be responsible for the interface state creation. The studies were performed for the AlGaN/GaN metal-insulator-semiconductor heterostructures (MISH) with Al2O3 and SiO2 dielectric films and AlxGa1-x layers with x varying from 0.15 to 0.4 as well as for an Al2O3/InAlN/GaN MISH structure. For all structures, it was found that: (i) D-it(E) is an U-shaped continuum increasing from the midgap towards the CB and VB edges and (ii) interface states near the VB exhibit donor-like character. Furthermore, D-it(E) for SiO2/AlxGa1-x/GaN structures increased with rising x. It was also revealed that carbon impurities are not present in the oxide/III-N interface region, which indicates that probably the interface states are not related to carbon, as previously reported. Finally, it was proven that the obtained D-it(E) spectrum can be well fitted using a formula predicted by the disorder induced gap state model. This is an indication that the interface states at oxide/III-N interfaces can originate from the structural disorder of the interfacial region. Furthermore, at the oxide/barrier interface we revealed the presence of the positive fixed charge (Q(F)) which is not related to D-it(E) and which almost compensates the negative polarization charge (Q(pol)(-))

Benchmark Rovibrational Linelists and Einstein A-coefficients for the Primordial Molecules and Isotopologues

Complete benchmark rovibrational energy linelists calculated for the primordial polar molecules of the universe, namely HD+, HD, and the HeH+ isotopologues, with accuracy up to 10(-2) cm(-1) for low-lying states, are presented. To allow for these calculations to be performed, new high-accuracy potential energy curves, which include the diagonal Born-Oppenheimer adiabatic corrections and the leading relativistic corrections, are determined. Also, a new approach for calculating non-adiabatic corrections involving an effective vibrational nuclear mass obtained based on the atoms-in-molecules theory is employed. The vibrational and rotational masses are taken as being different and dependent on the nuclear distance. Accurate dipole moment curves are calculated and used to generate lists of Einstein A-coefficients. The energy linelists and the sets of Einstein A-coefficients for HD are upgrades of previous calculations including quasibound states, while for HD+ and HeH+ and its isotopologues the present results represent significant improvement over the previous calculations. The results obtained here suggest that, with the inclusion of the non-adiabatic corrections, the accuracy limit at least for low-lying states might have been reached. Thus, further progress should involve accounting for even smaller effects such as the quantum-electrodynamics corrections. The present results represent the state-of-the-art of theoretical spectroscopy of the primordial polar molecules.CAPES; Polish National Science Centre [DEC-2013/10/E/ST4/00033]; CNPqThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Evolutionary Reduction of the First Thoracic Limb in Butterflies

Members of the diverse butterfly families Nymphalidae (brush-footed butterflies) and Riodinidae (metalmarks) have reduced first thoracic limbs and only use two pairs of legs for walking. In order to address questions about the detailed morphology and evolutionary origins of these reduced limbs, the three thoracic limbs of 13 species of butterflies representing all six butterfly families were examined and measured, and ancestral limb sizes were reconstructed for males and females separately. Differences in limb size across butterflies involve changes in limb segment size rather than number of limb segments. Reduction of the first limb in both nymphalids and riodinids appears particularly extensive in the femur, but the evolution of these reduced limbs is suggested to be a convergent evolutionary event. Possible developmental differences as well as ecological factors driving the evolution of reduced limbs are discussed

Non-Born-Oppenheimer calculations of the lowest vibrational energy of HD including relativistic corrections

In this work we report variational calculations of the two lowest vibrational states of the HD molecule within the framework that does not assume the Born-Oppenheimer BO approximation. The nonrelativistic energies of the states were corrected for the relativistic effects of the order of 2 where = 1 c , calculated as expectation values of the operators representing these effects with the nonrelativistic non-BO wave functions. The non-BO wave functions were expanded in terms of the one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. The v=0→1 transition energy obtained in the calculations is compared with the previous calculations, as well as with the transition frequency obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in to further improve the agreement between the theory and the experimen

Riemann-Cartan Space-times of G\"odel Type

A class of Riemann-Cartan G\"odel-type space-times are examined in the light of the equivalence problem techniques. The conditions for local space-time homogeneity are derived, generalizing previous works on Riemannian G\"odel-type space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this class is studied. It is shown that they admit a five-dimensional group of affine-isometries and are characterized by three essential parameters $\ell, m^2, \omega$: identical triads ($\ell, m^2, \omega$) correspond to locally equivalent manifolds. The algebraic types of the irreducible parts of the curvature and torsion tensors are also presented.Comment: 24 pages, LaTeX fil

Measuring price elasticities of demand and supply of water entitlements based on stated and revealed preference data

Estimates of price elasticities of water entitlements, known as permanent water or water rights in the United States, are complicated by data limitations and problems of endogeneity. To overcome these issues, we develop an approach to generate stated preference data and combine them with revealed preference data to estimate price elasticities from various types of water entitlement sales in the southern Murray-Darling Basin, Australia. Our results suggest that price elasticities of demand and supply of high security water entitlements are inelastic in the relevant market price range between AUD $1,700 to$2,100 per mega-liter, and that supply is relatively more inelastic than demand. For lower reliability water entitlements, the price elasticity of demand is estimated to be even more inelastic than high security water entitlements. The price elasticity of supply for general security water entitlements is similar to high security water entitlements, while the supply of low reliability water entitlements is extremely inelastic for our data set. The comparison between the stated and revealed preference data provides strong evidence of support for a data fusion approach, nevertheless, some differences in water sale preferences were found for irrigators choosing not to sell all of their water. The consistency of our results signals support for the use of this methodology in other water basins around the world.Alec Zuo, Sarah Ann Wheeler, W.L. (Vic) Adamowicz, Peter C. Boxall and Darla Hatton-MacDonal