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

Radiation Damage of F8 Lead Glass with 20 MeV Electrons

Using a 20 MeV linear accelerator, we investigate the effects of electromagnetic radiation on the optical transparency of F8 lead glass. Specifically, we measure the change in attenuation length as a function of radiation dose. Comparing our results to similar work that utilized a proton beam, we conclude that F8 lead glass is more susceptible to proton damage than electron damage.Comment: 5 pages, 6 figure

Quality of online self-management resources for adults living with primary brain cancer, and their carers: a systematic environmental scan

Background: A primary brain cancer diagnosis is a distressing, life changing event. It adversely affects the quality of life for the person living with brain cancer and their families (‘carers’). Timely access to evidence-based information is critical to enabling people living with brain cancer, and their carers, to self-manage the devastating impacts of this disease. Method: A systematic environmental scan of web-based resources. A depersonalised search for online English-language resources published from 2009 to December 2019 and designed for adults (> 25 years of age), living with primary brain cancer, was undertaken using the Google search engine. The online information was classified according to: 1) the step on the cancer care continuum; 2) self-management domains (PRISMS taxonomy); 3) basic information disclosure (Silberg criteria); 4) independent quality verification (HonCode); 5) reliability of disease and treatment information (DISCERN Sections 1 and 2); and readability (Flesch-Kincaid reading grade). Results: A total of 119 online resources were identified, most originating in England (n = 49); Australia (n = 27); or the USA (n = 27). The majority of resources related to active treatment (n = 76), without addressing recurrence (n = 3), survivorship (n = 1) or palliative care needs (n = 13). Few online resources directly provided self-management advice for adults living with brain cancer or their carers. Just over a fifth (n = 26, 22%) were underpinned by verifiable evidence. Only one quarter of organisations producing resources were HonCode certified (n = 9, 24%). The median resource reliability as measured by Section 1, DISCERN tool, was 56%. A median of 8.8 years of education was required to understand these online resources. Conclusions: More targeted online information is needed to provide people affected by brain cancer with practical self-management advice. Resources need to better address patient and carer needs related to: rehabilitation, managing behavioural changes, survivorship and living with uncertainty; recurrence; and transition to palliative care. Developing online resources that don’t require a high level of literacy and/or cognition are also required

Parton-Hadron Duality in Unpolarised and Polarised Structure Functions

We study the phenomenon of parton-hadron duality in both polarised and unpolarised electron proton scattering using the HERMES and the Jefferson Lab data, respectively. In both cases we extend a systematic perturbative QCD based analysis to the integrals of the structure functions in the resonance region. After subtracting target mass corrections and large x resummation effects, we extract the remaining power corrections up to order 1/Q^2. We find a sizeable suppression of these terms with respect to analyses using deep inelastic scattering data. The suppression appears consistently in both polarised and unpolarised data, except for the low Q^2 polarised data, where a large negative higher twist contribution remains. Possible scenarios generating this behavior are discussed.Comment: 17 pages, 9 figure

Phenomenology of Particle Production and Propagation in String-Motivated Canonical Noncommutative Spacetime

We outline a phenomenological programme for the search of effects induced by (string-motivated) canonical noncommutative spacetime. The tests we propose are based, in analogy with a corresponding programme developed over the last few years for the study of Lie-algebra noncommutative spacetimes, on the role of the noncommutativity parameters in the $E(p)$ dispersion relation. We focus on the role of deformed dispersion relations in particle-production collision processes, where the noncommutativity parameters would affect the threshold equation, and in the dispersion of gamma rays observed from distant astrophysical sources. We emphasize that the studies here proposed have the advantage of involving particles of relatively high energies, and may therefore be less sensitive to "contamination" (through IR/UV mixing) from the UV sector of the theory. We also explore the possibility that the relevant deformation of the dispersion relations could be responsible for the experimentally-observed violations of the GZK cutoff for cosmic rays and could have a role in the observation of hard photons from distant astrophysical sources.Comment: With respect to the experimental information available at the time of writing version 1 of this manuscript (hep-th/0109191v1) the situation has evolved significantly. Our remarks on the benefits of high-energy observations found additional encouragement from the results reported in hep-th/020925

United classification of cosmic gamma-ray bursts and their counterparts

United classification of gamma-ray bursts and their counterparts is established on the basis of measured characteristics: photon energy E and emission duration T. The founded interrelation between the mentioned characteristics of events consists in that, as the energy increases, the duration decreases (and vice versa). The given interrelation reflects the nature of the phenomenon and forms the E-T diagram, which represents a natural classification of all observed events in the energy range from 10E9 to 10E-6 eV and in the corresponding interval of durations from about 10E-2 up to 10E8 s. The proposed classification results in the consequences, which are principal for the theory and practical study of the phenomenon.Comment: Keywords Gamma rays: burst

Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model

We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte

Effect of the probiotic Lactobacilli reuteri (Prodentis) in the management of periodontal disease: a preliminary randomized clinical trial

Objectives: The aim of this study was to evaluate the effects of Lactobacilli reuteri (Prodentis) alone and in combination with scaling and root planing (SRP) in a double blind, randomized, placebo-controlled clinical trial of volunteers with chronic periodontitis. Methods: Thirty, otherwise systemically healthy, chronic periodontitis patients (19 males and 11 females, aged between 34 and 50 years) were included. The study period was 42 days. ‘Split-mouth’ design was used for the SRP, which was performed on day 0; two quadrants (either right or left) were treated with SRP whereas the remaining two quadrants were left untreated. The participants received a toothbrush, toothpaste, and brushing instructions. L. reuteri Prodentis lozenges (1×108 CFU DSM17938 + 1×108 CFU ATCC PTA 5289) or the corresponding placebo lozenges were taken twice daily from day 21 to day 42. Statistical analysis was done for comparisons of clinical parameters (Plaque Index (PI), Gingival Index (GI), Gingival Bleeding Index (GBI), probing pocket depth (PPD), clinical attachment level (CAL)) and microbiological levels of the pathogens Aggregibacter actinomycetemcomitans (Aa), Porphyromonas gingivalis (Pg), and Prevotella intermedia (Pi). All p-values less than 0.05 were considered significant. Assessments were made on day 0 before SRP treatment, on day 21 before administration of the lozenges, and on day 42. Results: At day 42, the PI, GI, and GBI were significantly reduced by all treatment modalities. When ranked, the amount of PI, GI and GBI reduction by the different treatments was SRP + Prodentis > Prodentis > SRP + placebo > placebo; all differences were statistically significant. For PPD and CAL, the best result was obtained with the SRP + Prodentis treatment. PPD was reduced from 5.08±0.75 to 3.78±0.61 mm (p<0.001) and CAL from 3.93±0.93 to 2.85±0.74 mm (p<0.001). Prodentis, either alone or following SRP, reduced Aa, Pi, and Pg by 1 log10 unit (p<0.01). The SRP + placebo combination did not significantly affect the levels of the pathogens. Conclusion: The present randomized controlled trial confirms the plaque inhibition, anti-inflammatory, and antimicrobial effects of L. reuteri Prodentis. L. reuteri Prodentis probiotic can be recommended during non-surgical therapy and the maintenance phase of periodontal treatment. Considering the beneficial effects of probiotics, this therapy could serve as a useful adjunct or alternative to periodontal treatment when SRP might be contraindicated. Further studies are required in this direction

Novel Druggable Hot Spots in Avian Influenza Neuraminidase H5N1 Revealed by Computational Solvent Mapping of a Reduced and Representative Receptor Ensemble

The influenza virus subtype H5N1 has raised concerns of a possible human pandemic threat because of its high virulence and mutation rate. Although several approved anti-influenza drugs effectively target the neuraminidase, some strains have already acquired resistance to the currently available anti-influenza drugs. In this study, we present the synergistic application of extended explicit solvent molecular dynamics (MD) and computational solvent mapping (CS-Map) to identify putative ‘hot spots’ within flexible binding regions of N1 neuraminidase. Using representative conformations of the N1 binding region extracted from a clustering analysis of four concatenated 40-ns MD simulations, CS-Map was utilized to assess the ability of small, solvent-sized molecules to bind within close proximity to the sialic acid binding region. Mapping analyses of the dominant MD conformations reveal the presence of additional hot spot regions in the 150- and 430-loop regions. Our hot spot analysis provides further support for the feasibility of developing high-affinity inhibitors capable of binding these regions, which appear to be unique to the N1 strain

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results