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    An overview of the effect of probiotics and exercise on mood and associated health conditions

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    The present paper provides a review of the current knowledge relating to the health benefits of probiotics, specially focused on the effects they may have together with physical exercise on mood disorders and related chronic medical conditions. With both these conditions being a substantial contributor to the global disease burden any alternative therapy must be considered. Probiotics influence the gut microbiota through a complex network of events which can influence mechanisms leading to development of mood disorders such as depression and anxiety. Similarly, through a complex interaction between psychological and neurobiological mechanisms, exercise has been found to play a key role in mood enhancement

    Stable divisorial gonality is in NP

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    Divisorial gonality and stable divisorial gonality are graph parameters, which have an origin in algebraic geometry. Divisorial gonality of a connected graph GG can be defined with help of a chip firing game on GG. The stable divisorial gonality of GG is the minimum divisorial gonality over all subdivisions of edges of GG. In this paper we prove that deciding whether a given connected graph has stable divisorial gonality at most a given integer kk belongs to the class NP. Combined with the result that (stable) divisorial gonality is NP-hard by Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof consist of a partial certificate that can be verified by solving an Integer Linear Programming instance. As a corollary, we have that the number of subdivisions needed for minimum stable divisorial gonality of a graph with nn vertices is bounded by 2p(n)2^{p(n)} for a polynomial pp