On the Structure of Solutions of Computable Real Functions

The relationship between the structure of a domain and the complexity of computing over that domain is a fundamental question of computer science. This paper studies how the structure of the real numbers constrains the behavior of computable real functions. In particular, we uncover a close correlation between the structure of the zero set of a computable real function, and the complexity of the zeros. We show that computable real functions with hard solutions perforce have many solutions. Furthermore, as the complexity of solutions increases, the number of solutions increases. We prove that computable real functions with nonrecursive, nonarithmetical, or random zeros have solution sets that are, respectively, infinite,“˜ uncountable, or of positive measure. In addition, we show that the computational complexity of the zero set of a computable real function is limited by its topological complexity. These results suggest an emerging paradigm-the inability of machines to name complex strings can serve as the basis of powerful proof techniques in computational complexity theory

On the Power of Probabilistic Polynomial Time: PNP[log] ⊆ PP

We show that every set in the ΘP2 level of the polynomial hierarchy -- that is, every set polynomial-time truth-table reducible to SAT -- is accepted by a probabilistic polynomialtime Turing machine: PNP[log] ⊆ PP

PAHs and star formation in the HII regions of nearby galaxies M83 and M33

We present mid-infrared (MIR) spectra of HII regions within star-forming galaxies M83 and M33. Their emission features are compared with Galactic and extragalactic HII regions, HII-type galaxies, starburst galaxies, and Seyfert/LINER type galaxies. Our main results are as follows: (i) the M33 and M83 HII regions lie in between Seyfert/LINER galaxies and HII-type galaxies in the 7.7/11.3 - 6.2/11.3 plane, while the different sub-samples exhibiting different 7.7/6.2 ratios; (ii) Using the NASA Ames PAH IR Spectroscopic database, we demonstrate that the 6.2/7.7 ratio does not effectively track PAH size, but the 11.3/3.3 PAH ratio does; (iii) variations on the 17 $\mu$m PAH band depends on object type; however, there is no dependence on metallicity for both extragalactic HII regions and galaxies; (iv) the PAH/VSG intensity ratio decreases with the hardness of the radiation field and galactocentric radius (Rg), yet the ionization alone cannot account for the variation seen in all of our sources; (v) the relative strength of PAH features does not change significantly with increasing radiation hardness, as measured through the [NeIII]/[NeII] ratio and the ionization index; (vi) We present PAH SFR calibrations based on the tight correlation between the 6.2, 7.7, and 11.3 $\mu$m PAH luminosities with the 24 $\mu$m luminosity and the combination of the 24 $\mu$m and H$\alpha$ luminosity; (vii) Based on the total luminosity from PAH and FIR emission, we argue that extragalactic HII regions are more suitable templates in modeling and interpreting the large scale properties of galaxies compared to Galactic HII regions.Comment: 26 pages, 24 figures, 6 tables. Accepted for publication in MNRA

On the Power of Parity Polynomial Time

This paper proves that the complexity class Ef)P, parity polynomial time [PZ83], contains the class of languages accepted by NP machines with few accepting paths. Indeed, Ef)P contains a. broad class of languages accepted by path-restricted nondeterministic machines. In particular, Ef)P contains the polynomial accepting path versions of NP, of the counting hierarchy, and of ModmNP for m > 1. We further prove that the class of nondeterministic path-restricted languages is closed under bounded truth-table reductions

An Assessment of the Social Science Research Environment of the Sri Lankan State University System

Higher education institutions play a vital role in society in varied capacities, and one major contribution amongst it all is conducting research as a part of knowledge creation and dissemination. Social Science Research thereby provides valuable input for policy makers, decision makers and the public, in order to encourage the well-being of the society. Previous studies have highlighted the importance of conducting social science researches to address social issues and improve quality of life. However, the number of research conducted in this discipline in Sri Lanka is not adequate when compared to that of other countries in the region. Hence, this study aims to explore the present status and challenges that hinder the number of social science research conducted by academics in State Universities in Sri Lanka. The study conducted a detailed literature review that was followed by in-depth interviews with 50 academics representing five state universities in Sri Lanka. The universities were selected based on the availability of Social Sciences and Humanities Faculties/Departments. The data were then analysed qualitatively based on the Grounded Theory Method to achievestudy objectives. The study revealed three main categories that limit the number of social science researches conducted in State Universities in Sri Lanka. They are; organizational factors, individual factors, and policy related factors. In addition, collaboration with other universities/ faculties, publication opportunities, research awards, and research allowance were identified as aspects in support of social science research in Sri Lanka. The study findings significantly helps in policy making, to identify the present status as well as factors that can contribute to enhance the level of social science related research among academics of State Universities in Sri Lanka.KeywordsResearch Environment, Social Sciences Research, State Universitie

Changes in cortical and striatal neurons predict behavioral and electrophysiological abnormalities in a transgenic murine model of Huntington\u27s disease

Neurons in Huntington\u27s disease exhibit selective morphological and subcellular alterations in the striatum and cortex. The link between these neuronal changes and behavioral abnormalities is unclear. We investigated relationships between essential neuronal changes that predict motor impairment and possible involvement of the corticostriatal pathway in developing behavioral phenotypes. We therefore generated heterozygote mice expressing the N-terminal one-third of huntingtin with normal (CT18) or expanded (HD46, HD100) glutamine repeats. The HD mice exhibited motor deficits between 3 and 10 months. The age of onset depended on an expanded polyglutamine length; phenotype severity correlated with increasing age. Neuronal changes in the striatum (nuclear inclusions) preceded the onset of phenotype, whereas cortical changes, especially the accumulation of huntingtin in the nucleus and cytoplasm and the appearance of dysmorphic dendrites, predicted the onset and severity of behavioral deficits. Striatal neurons in the HD mice displayed altered responses to cortical stimulation and to activation by the excitotoxic agent NMDA. Application of NMDA increased intracellular Ca(2+) levels in HD100 neurons compared with wild-type neurons. Results suggest that motor deficits in Huntington\u27s disease arise from cumulative morphological and physiological changes in neurons that impair corticostriatal circuitry

Anti-epileptic effect of Ganoderma lucidum polysaccharides by inhibition of intracellular calcium accumulation and stimulation of expression of CaMKII a in epileptic hippocampal neurons

Purpose: To investigate the mechanism of the anti-epileptic effect of Ganoderma lucidum polysaccharides (GLP), the changes of intracellular calcium and CaMK II a expression in a model of epileptic neurons were investigated. Method: Primary hippocampal neurons were divided into: 1) Control group, neurons were cultured with Neurobasal medium, for 3 hours; 2) Model group I: neurons were incubated with Mg2+ free medium for 3 hours; 3) Model group II: neurons were incubated with Mg2+ free medium for 3 hours then cultured with the normal medium for a further 3 hours; 4) GLP group I: neurons were incubated with Mg2+ free medium containing GLP (0.375 mg/ml) for 3 hours; 5) GLP group II: neurons were incubated with Mg2+ free medium for 3 hours then cultured with a normal culture medium containing GLP for a further 3 hours. The CaMK II a protein expression was assessed by Western-blot. Ca2+ turnover in neurons was assessed using Fluo-3/AM which was added into the replacement medium and Ca2+ turnover was observed under a laser scanning confocal microscope. Results: The CaMK II a expression in the model groups was less than in the control groups, however, in the GLP groups, it was higher than that observed in the model group. Ca2+ fluorescence intensity in GLP group I was significantly lower than that in model group I after 30 seconds, while in GLP group II, it was reduced significantly compared to model group II after 5 minutes. Conclusion: GLP may inhibit calcium overload and promote CaMK II a expression to protect epileptic neuron

The Complexity of Computing Minimal Unidirectional Covering Sets

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward or downward covering set. For both problems, we raise this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other natural problems regarding minimal or minimum-size covering sets are hard or complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of our results is that neither minimal upward nor minimal downward covering sets (even when guaranteed to exist) can be computed in polynomial time unless P=NP. This sharply contrasts with Brandt and Fischer's result that minimal bidirectional covering sets (i.e., sets that are both minimal upward and minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure