Galois groups of multivariate Tutte polynomials

The multivariate Tutte polynomial $\hat Z_M$ of a matroid $M$ is a generalization of the standard two-variable version, obtained by assigning a separate variable $v_e$ to each element $e$ of the ground set $E$. It encodes the full structure of $M$. Let \bv = \{v_e\}_{e\in E}, let $K$ be an arbitrary field, and suppose $M$ is connected. We show that $\hat Z_M$ is irreducible over K(\bv), and give three self-contained proofs that the Galois group of $\hat Z_M$ over K(\bv) is the symmetric group of degree $n$, where $n$ is the rank of $M$. An immediate consequence of this result is that the Galois group of the multivariate Tutte polynomial of any matroid is a direct product of symmetric groups. Finally, we conjecture a similar result for the standard Tutte polynomial of a connected matroid.Comment: 8 pages, final version, to appear in J. Alg. Comb. Substantial revisions, including the addition of two alternative proofs of the main resul

The relative importance of seed competition, resource competition and perturbations on community structure

While the regional climate is the primary selection pressure for whether a plant strategy can survive, however, competitive interactions strongly affect the relative abundances of plant strategies within communities. Here, we investigate the relative importance of competition and perturbations on the development of vegetation community structure. To do so, we develop DIVE (Dynamics and Interactions of VEgetation), a simple general model that links plant strategies to their competitive dynamics, using growth and reproduction characteristics that emerge from climatic constraints. The model calculates population dynamics based on establishment, mortality, invasion and exclusion in the presence of different strengths of perturbations, seed and resource competition. The highest levels of diversity were found in simulations without competition as long as mortality is not too high. However, reasonable successional dynamics were only achieved when resource competition is considered. Under high levels of competition, intermediate levels of perturbations were required to obtain coexistence. Since succession and coexistence are observed in plant communities, we conclude that the DIVE model with competition and intermediate levels of perturbation represents an adequate way to model population dynamics. Because of the simplicity and generality of DIVE, it could be used to understand vegetation structure and functioning at the global scale and the response of vegetation to global change

Altered States of Consciousness During Ceremonial San Pedro Use

San Pedro, a mescaline containing cactus, has been used for thousands of years and is currently popular as a psychedelic substance in ceremonial retreats in Europe. The current research investigates the consciousness altering effects of San Pedro. Forty-two participants who joined ceremonial psychedelic retreats in the Netherlands were investigated with questionnaires probing 11 dimensions of altered states of consciousness (11D-ASC), ego-dissolution, mystical experiences, and challenging experiences. Results tentatively demonstrate the status of San Pedro as a psychedelic, revealing deviations from normal waking consciousness on all 11 subscales of the 11D-ASC, moderate scores of ego-dissolution, and a complete mystical experience in two thirds of the participants. Furthermore, a consciousness profile of San Pedro was constructed, which revealed that spiritual experiences are strongly expressed in ceremonial San Pedro use. Furthermore, the San Pedro experience is characterized by low levels of disembodiment, anxiety, impaired control and cognition, transcendence of space, and relatively higher levels of physical distress and grief in case of (incidental) challenging experiences. Finally, graph network analysis indicated two separate networks of positive and negative altered states of consciousness. Possible interpretations of these findings are discussed in relation to the ceremonial setting, sympathomimetic effects of San Pedro?s alkaloids and variations in affective valence

Altered States of Consciousness During Ceremonial San Pedro Use

San Pedro, a mescaline containing cactus, has been used for thousands of years and is currently popular as a psychedelic substance in ceremonial retreats in Europe. The current research investigates the consciousness altering effects of San Pedro. Forty-two participants who joined ceremonial psychedelic retreats in the Netherlands were investigated with questionnaires probing 11 dimensions of altered states of consciousness (11D-ASC), ego-dissolution, mystical experiences, and challenging experiences. Results tentatively demonstrate the status of San Pedro as a psychedelic, revealing deviations from normal waking consciousness on all 11 subscales of the 11D-ASC, moderate scores of ego-dissolution, and a complete mystical experience in two thirds of the participants. Furthermore, a consciousness profile of San Pedro was constructed, which revealed that spiritual experiences are strongly expressed in ceremonial San Pedro use. Furthermore, the San Pedro experience is characterized by low levels of disembodiment, anxiety, impaired control and cognition, transcendence of space, and relatively higher levels of physical distress and grief in case of (incidental) challenging experiences. Finally, graph network analysis indicated two separate networks of positive and negative altered states of consciousness. Possible interpretations of these findings are discussed in relation to the ceremonial setting, sympathomimetic effects of San Pedro's alkaloids and variations in affective valence