New Deterministic Algorithms for Solving Parity Games

We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity games in time $k^{O(\sqrt{k})}\cdot O(n^3)$, and general parity games in time $(p+k)^{O(\sqrt{k})} \cdot O(pnm)$, where $p$ is the number of distinct priorities and $m$ is the number of edges. For all games with $k = o(n)$ this improves the previously fastest algorithm by Jurdzi{\'n}ski, Paterson, and Zwick (SICOMP 2008). We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree

An Exponential Lower Bound for the Latest Deterministic Strategy Iteration Algorithms

This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithms for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant improves every node in each step maximizing the current valuation locally, whereas the second variant computes the globally optimal improvement in each step. We outline families of games on which both variants require exponentially many strategy iterations

Symmetric Strategy Improvement

Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We develop a novel symmetric strategy improvement algorithm where, in each iteration, the strategies of both players are improved simultaneously. We show that symmetric strategy improvement defies Friedmann's traps, which shook the belief in the potential of classic strategy improvement to be polynomial

The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium of G where player 0 wins with probability 1. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if mixed strategies are allowed, decidability remains an open problem. One way to obtain a provably decidable variant of the problem is restricting the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively.Comment: 23 pages; revised versio

Local Strategy Improvement for Parity Game Solving

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy improvement algorithms. These are global in nature since they require the entire parity game to be present at the beginning. This is a distinct disadvantage because in many applications one only needs to know which winning region a particular node belongs to, and a witnessing winning strategy may cover only a fractional part of the entire game graph. We present a local strategy improvement algorithm which explores the game graph on-the-fly whilst performing the improvement steps. We also compare it empirically with existing global strategy improvement algorithms and the currently only other local algorithm for solving parity games. It turns out that local strategy improvement can outperform these others by several orders of magnitude

PND38 International Comparison of Huntington Disease (HD) Burden

n/

Imitation in Large Games

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation types: that of players who imitate choice of other (optimizing) types. Game theorists typically study the evolution of such games in dynamical systems with imitation rules. In the setting of games of infinite duration on finite graphs with preference orderings on outcomes for player types, we explore the possibility of imitation as a viable strategy. In our setup, the optimising players play bounded memory strategies and the imitators play according to specifications given by automata. We present algorithmic results on the eventual survival of types

Angiogenic Activity of Sera from Pulmonary Tuberculosis Patients in Relation to IL-12p40 and TNFα Serum Levels

The role of angiogenesis in the pathogenesis of tuberculosis (TB) is not clear. The aim of this study was to examine the effect of sera from TB patients on angiogenesis induced by different subsets of normal human mononuclear cells (MNC) in relation to IL-12p40 and TNFα serum levels. Serum samples from 36 pulmonary TB patients and from 22 healthy volunteers were evaluated. To assess angiogenic reaction the leukocytes-induced angiogenesis test according to Sidky and Auerbach was performed. IL-12p40 and TNFα serum levels were evaluated by ELISA. Sera from TB patients significantly stimulated angiogenic activity of MNC compared to sera from healthy donors and PBS (p < 0.001). The number of microvessels formed after injection of lymphocytes preincubated with sera from TB patients was significantly lower compared to the number of microvessels created after injection of MNC preincubated with the same sera (p < 0.016). However, the number of microvessels created after the injection of lymphocytes preincubated with sera from healthy donors or with PBS alone was significantly higher (p < 0.017). The mean levels of IL-12p40 and TNFα were significantly elevated in sera from TB patients compared to healthy donors. We observed a correlation between angiogenic activity of sera from TB patients and IL-12p40 and TNFα serum levels (p < 0.01). Sera from TB patients constitute a source of mediators that participate in angiogenesis and prime monocytes for production of proangiogenic factors. The main proangiogenic effect of TB patients’ sera is mediated by macrophages/monocytes. TNFα and IL-12p40 may indirectly stimulate angiogenesis in TB

Perfect Information Stochastic Priority Games

International audienceWe introduce stochastic priority games - a new class of perfect information stochastic games. These games can take two different, but equivalent, forms. In stopping priority games a play can be stopped by the environment after a finite number of stages, however, infinite plays are also possible. In discounted priority games only infinite plays are possible and the payoff is a linear combination of the classical discount payoff and of a limit payoff evaluating the performance at infinity. Shapley games and parity games are special extreme cases of priority games

Management practices, and not surrounding habitats, drive bird and arthropod biodiversity within vineyards

Agrochemical use and habitat loss associated with agriculture are drivers of biodiversity loss worldwide, and biodiversity-friendly farming practices, including organic management, are increasingly promoted by policy and industry in an attempt to offset this. Grapes are an important perennial crop globally, and in the UK, viticulture is the fastest growing agricultural sector and sustainable vineyard management is promoted by the Sustainable Wines of Great Britain ‘SWGB’ scheme. Here, we performed the first assessment of the simultaneous effects of surrounding habitats and vineyard management practices on bird and arthropod biodiversity across 22 English vineyards (10 certified-organic, 11 SWGB-accredited, and 3 both). We surveyed birds using point counts and arthropods with pitfall traps, and used linear mixed modelling to relate diversity and abundance to habitat and management predictors at landscape and local scales. We show that arthropod abundance is significantly higher on organic vineyards, whilst bird diversity is significantly lower on SWGB-accredited vineyards, but we find no other significant effects of organic certification or SWGB-accreditation on biodiversity. We also find no significant effects of the surrounding habitat structure on the biodiversity of birds and arthropods. Instead, we show that ecotoxicity scores derived from agrochemical use data have a significant negative impact on bird diversity, and on arthropod abundance and diversity. Organic status predicts a significant reduction in ecotoxicity scores, but only when application frequency is not considered, and contradictorily, SWGB-accredited vineyards have higher ecotoxicity scores than those without accreditation. Ground vegetation cover has a consistent, positive effect on bird and arthropod diversity, with model predicted diversity increasing 1.5 and 2.5-fold, respectively, in vineyards with the highest vegetation cover, and herbicide use has a negative effect on the vegetation cover. Our research demonstrates that individual management practices have a stronger effect on vineyard biodiversity than the habitat context, overall management regime or certification. Our study sets an important baseline for vineyard management and accreditation schemes and generates key recommendations for improvement. To benefit biodiversity within vineyards, we recommend that sustainability accreditation schemes include requirements to reduce the ecotoxicity of used agrochemicals, and promote higher ground vegetation cover and height by reducing herbicide use