An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares a number of approximation methods and exact methods. In particular, we explore the trade-off between the quality of approximate equilibrium and the required running time to find one. We found that the existing library GAMUT, which has been the de facto standard that has been used to test exact methods, is insufficient as a test bed for approximation methods since many of its games have pure equilibria or other easy-to-find good approximate equilibria. We extend the breadth and depth of our study by including new interesting families of bimatrix games, and studying bimatrix games upto size $2000 \times 2000$. Finally, we provide new close-to-worst-case examples for the best-performing algorithms for finding approximate Nash equilibria

Separable and Low-Rank Continuous Games

In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in separable games. We show that these games admit finitely supported Nash equilibria. Motivated by the bounds on the supports of mixed equilibria in two-player finite games in terms of the ranks of the payoff matrices, we define the notion of the rank of an n-player continuous game and use this to provide bounds on the cardinality of the support of equilibrium strategies. We present a general characterization theorem that states that a continuous game has finite rank if and only if it is separable. Using our rank results, we present an efficient algorithm for computing approximate equilibria of two-player separable games with fixed strategy spaces in time polynomial in the rank of the game

“It’s just a theory”: trainee science teachers’ misunderstandings of key scientific terminology

Background: This article presents the findings from a survey of 189 pre-service science teachers who were asked to provide definitions of key scientific terms ('theory'; 'fact'; 'law'; 'hypothesis'). The survey was a scoping and mapping exercise to establish the range and variety of definitions. Methods: Graduates on a pre-service science teacher training course were asked to complete a short, free response survey and define key science terminology a >95% response rate was achieved and respondents definitions were categorised according to a best fit model. Results: In some cases, definitions contrary to accepted scientific meanings were given. In other cases, terminology was defined in a wholly non-scientific way, e.g., one-fifth of the respondents defined a ‘law’ in the context of rules that govern society rather than in a scientific context. Science graduates’ definitions and their understanding of key terminology is poor despite their study of science in formal university settings (with many respondents being recent science graduates). Conclusions: Key terminology in science, such as 'theory', 'law', 'fact', 'hypothesis', tends not to be taught and defined with consideration for the differences in meaning that different audiences/users give to them. This article calls for better instruction for pre-service science teachers’ in the importance of accurate and precise definitions of key science terminology in order to better differentiate between the scientific and colloquial usage of key terms

In vitro assessment of adsorbents aiming to prevent deoxynivalenol and zearalenone mycotoxicoses

The high prevalence of the Fusarium mycotoxins, deoxynivalenol (DON) and zearalenone (ZON) in animal feeds in mild climatic zones of Europe and North America results in considerable economic losses, as these toxins affect health and productivity particularly of pigs from all age groups. The use of mycotoxin adsorbents as feed additives is one of the most prominent approaches to reduce the risk for mycotoxicoses in farm animals, and to minimise carry-over of mycotoxins from contaminated feeds into foods of animal origin. Successful aflatoxin adsorption by means of different substances (phyllosilicate minerals, zeolites, activated charcoal, synthetic resins or yeast cell-wall-derived products) has been demonstrated in vivo and in vitro. However, attempts to adsorb DON and ZON have been less encouraging. Here we describe the adsorption capacity of a variety of potential binders, including compounds that have not been evaluated before, such as humic acids. All compounds were tested at realistic inclusion levels for their capacity to bind ZON and DON, using an in vitro method that resembles the different pH conditions in the gastro-intestinal tract of pigs. Mycotoxin adsorption was assessed by chemical methods and distinct bioassays, using specific markers of toxicity as endpoints of toxicity in cytological assays. Whereas none of the tested substances was able to bind DON in an appreciable percentage, some of the selected smectite clays, humic substances and yeast-wall derived products efficiently adsorbed ZON (>70%). Binding efficiency was indirectly confirmed by the reduction of toxicity in the in vitro bioassays. In conclusion, the presented test protocol allows the rapid screening of potential mycotoxin binders. Like other in vitro assays, the presented protocol combining chemical and biological assays cannot completely simulate the conditions of the gastro-intestinal tract, and hence in vivo experiments remain mandatory to assess the efficacy of mycotoxin binders under practical conditions

Impact of comorbid psychiatric disorders on the outcome of substance abusers: a six year prospective follow-up in two Norwegian counties

BACKGROUND: Most help-seeking substance abusers have comorbid psychiatric disorders. The importance of such disorders for the long-term course of substance abuse is, however, still unclear. The aim of this paper is to describe six-year outcomes regarding death and relapse among alcoholics and poly-substance abusers and to analyse the predictive value of lifetime psychiatric disorders on relapse. METHODS: A consecutive sample of substance-dependent patients who received treatment in two counties in Norway (n = 287) was followed up after approximately six years. Information on socio-demographics, Axis I (CIDI) and II disorders (MCMI-II) and mental distress (HSCL-25) was gathered at baseline. At follow-up, detailed information regarding socio-demographics, use of substances (AUDIT and DUDIT) and mental distress (HSCL-25) was recorded (response rate: 63%). RESULTS: At six-year follow-up, 11% had died, most often male alcoholics (18%). Among the surviving patients, 70% had drug or alcohol related problems the year prior to follow-up. These patients were, classified as "relapsers". There were no significant differences in the relapse rate between women and men and among poly-substance abusers and alcoholics. The relapsers had an earlier onset of a substance use disorder, and more frequently major depression and agoraphobia. Multivariate analysis indicated that both psychiatric disorders (major depression) and substance use factors (early onset of a substance use disorder) were independent predictors of relapse. CONCLUSION: For reducing the risk of long-term relapse, assessment and treatment of major depression (and agoraphobia) are important. In addition, we are in need of a comprehensive treatment and rehabilitation program that also focuses on the addictive behaviour

Nε−Lysine Acetylation of a Bacterial Transcription Factor Inhibits Its DNA-Binding Activity

Evidence suggesting that eukaryotes and archaea use reversible Nε-lysine (Nε-Lys) acetylation to modulate gene expression has been reported, but evidence for bacterial use of Nε-Lys acetylation for this purpose is lacking. Here, we report data in support of the notion that bacteria can control gene expression by modulating the acetylation state of transcription factors (TFs). We screened the E. coli proteome for substrates of the bacterial Gcn5-like protein acetyltransferase (Pat). Pat acetylated four TFs, including the RcsB global regulatory protein, which controls cell division, and capsule and flagellum biosynthesis in many bacteria. Pat acetylated residue Lys180 of RcsB, and the NAD+-dependent Sir2 (sirtuin)-like protein deacetylase (CobB) deacetylated acetylated RcsB (RcsBAc), demonstrating that Nε-Lys acetylation of RcsB is reversible. Analysis of RcsBAc and variant RcsB proteins carrying substitutions at Lys180 provided biochemical and physiological evidence implicating Lys180 as a critical residue for RcsB DNA-binding activity. These findings further the likelihood that reversible Nε-Lys acetylation of transcription factors is a mode of regulation of gene expression used by all cells

Finite-Step Algorithms for Single-Controller and Perfect Information Stochastic Games

Abstract. After a brief survey of iterative algorithms for general stochas-tic games, we concentrate on finite-step algorithms for two special classes of stochastic games. They are Single-Controller Stochastic Games and Per-fect Information Stochastic Games. In the case of single-controller games, the transition probabilities depend on the actions of the same player in all states. In perfect information stochastic games, one of the players has exactly one action in each state. Single-controller zero-sum games are effi-ciently solved by linear programming. Non-zero-sum single-controller stochastic games are reducible to linear complementary problems (LCP). In the discounted case they can be modified to fit into the so-called LCPs of Eave’s class L. In the undiscounted case the LCP’s are reducible to Lemke’s copositive plus class. In either case Lemke’s algorithm can be used to find a Nash equilibrium. In the case of discounted zero-sum perfect informa-tion stochastic games, a policy improvement algorithm is presented. Many other classes of stochastic games with orderfield property still await efficient finite-step algorithms. 1

The use and limits of ITS data in the analysis of intraspecific variation in Passiflora L. (Passifloraceae)

The discovery and characterization of informative intraspecific genetic markers is fundamental for evolutionary and conservation genetics studies. Here, we used nuclear ribosomal ITS sequences to access intraspecific genetic diversity in 23 species of the genus Passiflora L. Some degree of variation was detected in 21 of these. The Passiflora and Decaloba (DC.) Rchb. subgenera showed significant differences in the sizes of the two ITS regions and in GC content, which can be related to reproductive characteristics of species in these subgenera. Furthermore, clear geographical patterns in the spatial distribution of sequence types were identified in six species. The results indicate that ITS may be a useful tool for the evaluation of intraspecific genetic variation in Passiflora