The Computational Complexity of the Game of Set and its Theoretical Applications

The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and establish interesting connections with other classical computational problems. Specifically, we first show that a natural generalization of the problem of finding a single Set, parameterized by the size of the sought Set is W-hard; our reduction applies also to a natural parameterization of Perfect Multi-Dimensional Matching, a result which may be of independent interest. Second, we observe that a version of the game where one seeks to find the largest possible number of disjoint Sets from a given set of cards is a special case of 3-Set Packing; we establish that this restriction remains NP-complete. Similarly, the version where one seeks to find the smallest number of disjoint Sets that overlap all possible Sets is shown to be NP-complete, through a close connection to the Independent Edge Dominating Set problem. Finally, we study a 2-player version of the game, for which we show a close connection to Arc Kayles, as well as fixed-parameter tractability when parameterized by the number of rounds played

Unsteady Full Annulus Simulations of a Transonic Axial Compressor Stage

Two recent research endeavors in turbomachinery at NASA Glenn Research Center have focused on compression system stall inception and compression system aerothermodynamic performance. Physical experiment and computational research are ongoing in support of these research objectives. TURBO, an unsteady, three-dimensional, Navier-Stokes computational fluid dynamics code commissioned and developed by NASA, has been utilized, enhanced, and validated in support of these endeavors. In the research which follows, TURBO is shown to accurately capture compression system flow range-from choke to stall inception-and also to accurately calculate fundamental aerothermodynamic performance parameters. Rigorous full-annulus calculations are performed to validate TURBO s ability to simulate the unstable, unsteady, chaotic stall inception process; as part of these efforts, full-annulus calculations are also performed at a condition approaching choke to further document TURBO s capabilities to compute aerothermodynamic performance data and support a NASA code assessment effort

Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid

The mechanical response and load bearing capacity of high performance polymer composites changes due to diffusion of a fluid, temperature, oxidation or the extent of the deformation. Hence, there is a need to study the response of bodies under such degradation mechanisms. In this paper, we study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent. We specifically investigate the torsion of a generalized neo-Hookean circular cylindrical annulus infused with a fluid. The equations of equilibrium for a generalized neo-Hookean solid are solved together with the convection-diffusion equation for the fluid concentration. Different boundary conditions for the fluid concentration are also considered. We also solve the problem for the case when the diffusivity of the fluid depends on the deformation of the generalized neo-Hookean solid.Comment: 24 pages, 10 figures, submitted to Mechanics of Time-dependent Material

Results of the MRI substudy of the intravenous magnesium efficacy in stroke trial

<p><b>Background and Purpose:</b>Although magnesium is neuroprotective in animal stroke models, no clinical benefit was confirmed in the Intravenous Magnesium Efficacy in Stroke (IMAGES) trial of acute stroke patients. The Magnetic Resonance in IMAGES (MR IMAGES) substudy investigated the effects of magnesium on the imaging surrogate outcome of infarct growth.</p> <p><b>Methods:</b> IMAGES trial patients in participating centers were randomized to receive either intravenous magnesium or placebo within 12 hours of stroke onset. Infarct growth was defined as volume difference between baseline diffusion-weighted imaging and day 90 fluid-attenuated inversion recovery image lesions. Patients who died were imputed the largest infarct growth observed.</p> <p><b>Results:</b> Among the 90 patients included in the primary analysis, there was no difference in infarct growth (median absolute growth, P=0.639; median percentage growth, P=0.616; proportion with any growth, P=0.212) between the 46 treated with magnesium and 44 with placebo. Infarct growth correlated with NIHSS score change from baseline to day 90. There was a trend showing baseline serum glucose correlated with infarct growth with magnesium treatment, but not in the placebo group. The mismatch frequency was reduced from 73% to 47% by increasing the mismatch threshold from >20% to >100% of core volume.</p> <p><b>Conclusions:</b> Infarct growth, confirmed here as a surrogate for clinical progression, was similar between magnesium and placebo treatment, paralleling the main IMAGES trial clinical outcomes. Glucose was a covariate for infarct growth with magnesium treatment. A more stringent mismatch threshold to define penumbra more appropriately would have excluded half of the patients in this 12-hour time window stroke study.</p&gt

Ultraviolet (UV) B effects on growth and yield of three contrasting sweet potato cultivars

Ground-level UV-B will stay at a high level in the next several decades and influence sweet potato growth and yield because of the remaining chlorofluorocarbons in the atmosphere. The study explored three UV-B (none, ambient, and elevated/projected) levels on three contrasting sweet potato cultivars (Beauregard, Hatteras, and Louisiana 1188) using sunlit plant growth chambers at Mississippi State University. The results showed that UV-B influenced three cultivars differently. Growth, photosynthetic rate, epidermal and leaf structure of Beauregard were negatively influenced under ambient and elevated UV-B. On the contrary, Hatteras was positively influenced, and Louisiana 1188 was influenced by elevated UV-B positively on leaf thickness and waxes content, but negatively on the vine length, dry mass, and leaf area. In summary, Beauregard, Louisiana 1188, and Hatteras were UV-B sensitive, moderately sensitive, and tolerant, respectively. Developing UV-B tolerant cultivars will benefit under both current and projected UV-B exposures

Sequential pivotal mechanisms for public project problems

It is well-known that for several natural decision problems no budget balanced Groves mechanisms exist. This has motivated recent research on designing variants of feasible Groves mechanisms (termed as `redistribution of VCG (Vickrey-Clarke-Groves) payments') that generate reduced deficit. With this in mind, we study sequential mechanisms and consider optimal strategies that could reduce the deficit resulting under the simultaneous mechanism. We show that such strategies exist for the sequential pivotal mechanism of the well-known public project problem. We also exhibit an optimal strategy with the property that a maximal social welfare is generated when each player follows it. Finally, we show that these strategies can be achieved by an implementation in Nash equilibrium.Comment: 19 pages. The version without the appendix will appear in the Proc. 2nd International Symposium on Algorithmic Game Theory, 200

Gauge coupling flux thresholds, exotic matter and the unification scale in F-SU(5) GUT

We explore the gauge coupling relations and the unification scale in F-theory SU(5) GUT broken down to the Standard Model by an internal U(1)Y gauge flux. We consider variants with exotic matter representations which may appear in these constructions and investigate their role in the effective field theory model. We make a detailed investigation on the conditions imposed on the extraneous matter to raise the unification scale and make the color triplets heavy in order to avoid fast proton decay. We also discuss in brief the implications on the gaugino masses.Comment: 20 pages, 3 figures, references and extended comments on KK thresholds effects adde

Functional characterization of three genes encoding putative oxidoreductases required for cercosporin toxin blosynthesis in the fungus Cercospora nicotianae

Cercosporin is a non-host-selective, photoactivated polyketide toxin produced by many phytopathogenic Cercospora species, which plays a crucial role during pathogenesis on host plants. Upon illumination, cercosporin converts oxygen molecules to toxic superoxide and singlet oxygen that damage various cellular components and induce lipid peroxidation and electrolyte leakage. Three genes (CTB5, CTB6 and CTB7) encoding putative FAD/FMN- or NADPH-dependent oxidoreductases in the cercosporin toxin biosynthetic pathway of C. nicotianae were functionally analysed. Replacement of. each gene via double recombination was utilized to create null mutant strains that were completely impaired in cercosporin production as a consequence of specific interruption at the CTB5, CTB6 or CTB7 locus. Expression of CTB1, CTB5, CTB6, CTB7 and CTB8 was drastically reduced or nearly abolished when CTB5, CTB6 or CTB7 was disrupted. Production of cercosporin was revived when a functional gene cassette was introduced into the respective mutants. All ctb5, ctb6 and ctb7 null mutants retained wild-type levels of resistance against toxicity of cercosporin or singlet-oxygen-generating compounds, indicating that none of the genes plays a role in self-protection

Mediators of the association between educational attainment and type 2 diabetes mellitus:a two-step multivariable Mendelian randomisation study

Aims/hypothesis: Type 2 diabetes mellitus is a major health burden disproportionately affecting those with lower educational attainment (EA). We aimed to obtain causal estimates of the association between EA and type 2 diabetes and to quantify mediating effects of known modifiable risk factors. Methods: We applied two-step, two-sample multivariable Mendelian randomisation (MR) techniques using SNPs as genetic instruments for exposure and mediators, thereby minimising bias due to confounding and reverse causation. We leveraged summary data on genome-wide association studies for EA, proposed mediators (i.e. BMI, blood pressure, smoking, television watching) and type 2 diabetes. The total effect of EA on type 2 diabetes was decomposed into a direct effect and indirect effects through multiple mediators. Additionally, traditional mediation analysis was performed in a subset of the National Health and Nutrition Examination Survey 2013–2014. Results: EA was inversely associated with type 2 diabetes (OR 0.53 for each 4.2 years of schooling; 95% CI 0.49, 0.56). Individually, the largest contributors were BMI (51.18% mediation; 95% CI 46.39%, 55.98%) and television watching (50.79% mediation; 95% CI 19.42%, 82.15%). Combined, the mediators explained 83.93% (95% CI 70.51%, 96.78%) of the EA–type 2 diabetes association. Traditional analysis yielded smaller effects but showed consistent direction and priority ranking of mediators. Conclusions/interpretation: These results support a potentially causal protective effect of EA against type 2 diabetes, with considerable mediation by a number of modifiable risk factors. Interventions on these factors thus have the potential of substantially reducing the burden of type 2 diabetes attributable to low EA