Microbial trace fossils in Antarctica and the search for evidence of early life on Mars

It is possible to hypothesize that, if microbial life evolved on early Mars, fossil remnants of these organisms may be preserved on the surface. However, the cooling and drying of Mars probably resembled a cold desert and such an environment is not suitable for the process of fossilization. The frigid Ross Desert of Antarctica is probably the closest terrestrial analog to conditions that may have prevailed on the surface of the cooling and drying Mars. In this desert, cryptoendolithic microbial communities live in the airspaces of porous rocks, the last habitable niche in a hostile outside environment. The organisms produce characteristic chemical and physical changes in the rock substrate. Environmental changes (deterioration of conditions) may result in the death of the community. Although no cellular structures are fossilized, the conspicuous changes in the rock substrate are preserved as trace fossils. Likewise, microbial trace fossils (without cellular structures) may also be preserved on Mars: Discontinuities in structure or chemistry of the rock that are independent of physical or chemical gradients may be of biological origin. Ross Desert trace fossils can be used as a model for planning search strategies and for instrument design to find evidence of past Martian life

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

Combinatorial simplex algorithms can solve mean payoff games

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff games. Moreover, any combinatorial simplex algorithm with a strongly polynomial complexity (the existence of such an algorithm is open) would provide in this way a strongly polynomial algorithm solving mean payoff games. Mean payoff games are known to be in NP and co-NP; whether they can be solved in polynomial time is an open problem. Our algorithm relies on a tropical implementation of the simplex method over a real closed field of Hahn series. One of the key ingredients is a new scheme for symbolic perturbation which allows us to lift an arbitrary mean payoff game instance into a non-degenerate linear program over Hahn series.Comment: v1: 15 pages, 3 figures; v2: improved presentation, introduction expanded, 18 pages, 3 figure

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

Bulk Scale Factor at Very Early Universe

In this paper we propose a higher dimensional Cosmology based on FRW model and brane-world scenario. We consider the warp factor in the brane-world scenario as a scale factor in 5-dimensional generalized FRW metric, which is called as bulk scale factor, and obtain the evolution of it with space-like and time-like extra dimensions. It is then showed that, additional space-like dimensions can produce exponentially bulk scale factor under repulsive strong gravitational force in the empty universe at a very early stage.Comment: 7 pages, October 201

Polynomial Hamiltonian form of General Relativity

Phase space of General Relativity is extended to a Poisson manifold by inclusion of the determinant of the metric and conjugate momentum as additional independent variables. As a result, the action and the constraints take a polynomial form. New expression for the generating functional for the Green functions is proposed. We show that the Dirac bracket defines degenerate Poisson structure on a manifold, and a second class constraints are the Casimir functions with respect to this structure. As an application of the new variables, we consider the Friedmann universe.Comment: 33 pages, 1 figure, corrected reference