Black holes, complexity and quantum chaos

We study aspects of black holes and quantum chaos through the behavior of computational costs, which are distance notions in the manifold of unitaries of the theory. To this end, we enlarge Nielsen geometric approach to quantum computation and provide metrics for finite temperature/energy scenarios and CFT's. From the framework, it is clear that costs can grow in two different ways: operator vs `simple' growths. The first type mixes operators associated to different penalties, while the second does not. Important examples of simple growths are those related to symmetry transformations, and we describe the costs of rotations, translations, and boosts. For black holes, this analysis shows how infalling particle costs are controlled by the maximal Lyapunov exponent, and motivates a further bound on the growth of chaos. The analysis also suggests a correspondence between proper energies in the bulk and average `local' scaling dimensions in the boundary. Finally, we describe these complexity features from a dual perspective. Using recent results on SYK we compute a lower bound to the computational cost growth in SYK at infinite temperature. At intermediate times it is controlled by the Lyapunov exponent, while at long times it saturates to a linear growth, as expected from the gravity description.Comment: 30 page

Black holes as random particles: entanglement dynamics in infinite range and matrix models

We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-$\mathcal{N}$ matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-$\mathcal{N}$ matrix models, where we provide a gauge invariant entanglement entropy for `generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.Comment: Journal versio

Integrating gene expression, ecology and mycotoxin production by Fusarium and Aspergillus species in relation to interacting environmental factors

Environmental factors, such as water availability (water activity, aw), temperature and their interactions, have a significant impact on the life cycle of mycotoxigenic fungi. Growth and mycotoxin production are influenced by these interacting factors resulting in a broader range of aw × temperature conditions for germination, than growth or mycotoxin production. The biosynthetic genes are mostly clustered together and by using microarrays with sub-arrays for specific mycotoxins, such as trichothecenes, fumonisins and aflatoxins it has been possible to examine the relationship between interacting aw × temperature conditions on growth, toxin gene cluster expression and relate these to phenotypic toxin production. The data for groups of biosynthetic genes (Fusarium culmorum/Fusarium graminearum; Fusarium verticillioides; Aspergillus flavus) were integrated with data on growth and mycotoxin production under different aw × temperature conditions using a mixed growth model. This was used to correlate these factors and predict toxin levels which may be produced under different abiotic stress conditions. Indeed, the relative importance of the different genes could be examined using ternary diagrams of the relative expression of 3 genes at a time in relation to aw, temperature and mycotoxin production to identify the most important relationships. The effect of three-way interacting environmental factors representative of climate change (CC) scenarios (water stress × temperature (+2-4 °C) × elevated CO2 (350-400 vs 650 and 1000 ppm) on growth and mycotoxin production by A. flavus and by species of the Aspergillus section Circumdati and section Nigri have been determined. These studies on maize grain and coffee, respectively, suggest that while growth may not be significantly affected, mycotoxin production may be stimulated by CC factors. This approach to integrate such data sets and model the relationships could be a powerful tool for predicting the relative toxin production under extreme stress conditions, including CC scenarios

Foreword: mycotoxins in a changing world

This special issue arose because of the changes in the global landscape in relation to the impact and implications of our changing climate on food security and quality, consumer habits, trade and economics, regulations and scientific thinking. The EU green paper (EC, 2007) on climate change (CC) has suggested significant hot spots in different regions where food production will be considerably affected both in quality and quantity. Indeed, a recent UNEP report on ‘Emerging Issues of Environmental Concern’ (UNEP, 2016) has included a section entitled ‘Poisoned chalice: Toxin accumulation in crops in an era of climate change’ which refers to the impact that aflatoxin contamination is having in low and middle income countries (LMICs)

Environmental factors modify carbon nutritional patterns and niche overlap between Aspergillus flavus and Fusarium verticillioides strains from maize.

This study examined the utilization patterns of key carbon sources (CS, 24: including key sugars, amino acids and fatty acids) in maize by strains of Aspergillus flavus and Fusarium verticillioides under different water activity (aw, 0.87–0.98 aw) and temperature (20–35 °C) values and compared the niche overlap indices (NOI) that estimate the in vitro CS utilization profiles [Wilson, M., Lindow, S.E., 1994. Coexistence among epiphytic bacterial populations mediated through nutritional resource partitioning. Applied and Environmental Microbiology 60, 4468–4477.]. The ability to grow in these key CS in minimal media was studied for 120 h in 12 h steps. The NOI was calculated for inter-species (F. verticillioides–A. flavus) and for intra-species (A. flavus–A. flavus) using CS utilization patterns over the range of interacting environmental conditions. 30 °C, over the whole aw range examined, was found to be optimal for utilization of the maximum number of CS by A. flavus. In contrast, for F. verticillioides this was more so at 20 °C; 25 °C allowed a suboptimal usage of CS for both species. NOIs confirmed the nutritional dominance of A. flavus at 30 °C, especially at lower aw levels and that of F. verticillioides at 20 °C, mainly at 0.95 aw. In other conditions of aw, based on CS utilization patterns, the data indicated that A. flavus and F. verticillioides occupied different ecological niches. The variability in nutritional sources utilization between A. flavus strains was not related to their ability to produce aflatoxins (AFs). This type of data helps to explain the nutritional dominance of fungal species and strains under different environmental conditions. This could be useful in trying to find appropriate natural biocontrol microorganisms to compete with these mycotoxigenic species