Analytic Loops and Gauge Fields

In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We show that such representations are closely associated with the (anti-)self-dual Yang-Mills equations in ${\bf R}^8$Comment: 10 pages, LaTeX, no figure

On n-ary Hom-Nambu and Hom-Nambu-Lie algebras

It is observed that the category of n-ary Hom-Nambu(-Lie) algebras is closed under twisting by self-weak morphisms. Constructions of ternary Hom-Nambu algebras from Hom-associative algebras, Hom-Lie algebras, ternary totally Hom-associative algebras, and Hom-Jordan triple systems are given. Every multiplicative n-ary Hom-Nambu algebra gives rise to a sequence of Hom-Nambu algebras of exponentially higher arities. Under some conditions, an n-ary Hom-Nambu(-Lie) algebra gives rise to an (n-1)-ary Hom-Nambu(-Lie) algebra.Comment: 23 page

The meeting of one hundred ways

In this dissertation the following topics are examined: (1) The possible scientific and archetypal causes and resulting effects of disembodiment and fragmentation of the Western mind/psyche; (2) the possible causes and effects of a multifaceted split between mother and infant predominant in the Western world; and (3) the interrelation of the above-mentioned subjects and their influences on our world as we know it. This work draws on the disciplines of: history, art, depth psychology, archetypal psychology, neurobiology, and nonlinear dynamics theory. The emphasis is on drawing attention to a paradox encompassing both the immeasurable fragmentation and the infinitesimal interrelation of every being and every thing and on challenging the prevalent approach of reductionism and static linearity, driven by mechanistic science, which often stands in contrast to the discoveries of new science, by illuminating the chaos within the dynamic structure of the universe. First, we examine the historical significance of a shift toward mechanistic science, which led to a widely held belief in the Cartesian mind/matter split. Next, through the lens of neuroscience, we learn about the essentials of attachment theory, regulation, and brain development, which are then applied to the topic of the mother-infant bond. Subsequently, we study the contribution of an archetypal pull toward the shift in the direction of mechanistic science and present an overview of the fundamental findings of nonlinear dynamics theory as they relate to both attachment and regulation of the mother-infant bond. Further details are provided by introducing notions of psychic phenomenon, intuition, and synchronicity. From that perspective we again delve into the subjects of attachment and regulation now presented on an infinitesimal scale of gene expression. This summarizes an endeavor to contribute to the depth psychological perspective by shedding some light on various ways of re-uniting and incorporating into it the practices of other healing professions as well as scientific discoveries. Additionally, it is an attempt to ignite a sense of wonder in those who have not yet examined the abovementioned subjects

Non-destructive quantification of anaerobic gut fungi and methanogens in co-culture reveals increased fungal growth rate and changes in metabolic flux relative to mono-culture.

BackgroundQuantification of individual species in microbial co-cultures and consortia is critical to understanding and designing communities with prescribed functions. However, it is difficult to physically separate species or measure species-specific attributes in most multi-species systems. Anaerobic gut fungi (AGF) (Neocallimastigomycetes) are native to the rumen of large herbivores, where they exist as minority members among a wealth of prokaryotes. AGF have significant biotechnological potential owing to their diverse repertoire of potent lignocellulose-degrading carbohydrate-active enzymes (CAZymes), which indirectly bolsters activity of other rumen microbes through metabolic exchange. While decades of literature suggest that polysaccharide degradation and AGF growth are accelerated in co-culture with prokaryotes, particularly methanogens, methods have not been available to measure concentrations of individual species in co-culture. New methods to disentangle the contributions of AGF and rumen prokaryotes are sorely needed to calculate AGF growth rates and metabolic fluxes to prove this hypothesis and understand its causality for predictable co-culture design.ResultsWe present a simple, microplate-based method to measure AGF and methanogen concentrations in co-culture based on fluorescence and absorbance spectroscopies. Using samples of < 2% of the co-culture volume, we demonstrate significant increases in AGF growth rate and xylan and glucose degradation rates in co-culture with methanogens relative to mono-culture. Further, we calculate significant differences in AGF metabolic fluxes in co-culture relative to mono-culture, namely increased flux through the energy-generating hydrogenosome organelle. While calculated fluxes highlight uncertainties in AGF primary metabolism that preclude definitive explanations for this shift, our method will enable steady-state fluxomic experiments to probe AGF metabolism in greater detail.ConclusionsThe method we present to measure AGF and methanogen concentrations enables direct growth measurements and calculation of metabolic fluxes in co-culture. These metrics are critical to develop a quantitative understanding of interwoven rumen metabolism, as well as the impact of co-culture on polysaccharide degradation and metabolite production. The framework presented here can inspire new methods to probe systems beyond AGF and methanogens. Simple modifications to the method will likely extend its utility to co-cultures with more than two organisms or those grown on solid substrates to facilitate the design and deployment of microbial communities for bioproduction and beyond

An Arduino based Automatic Pressure Evaluation System (A-APES) to quantify growth of non-model anaerobes in culture

Measuring the growth rate of non‐model anaerobic microbes typically requires the use of time‐consuming and often destructive manual measurements. Here, an Arduino based automatic pressure evaluation system (A‐APES) was developed to automatically measure the rate of fermentation gas production as a proxy for microbial growth in anaerobic systems. The A‐APES system measures accumulated gas pressure in sealed cultures accurately at high‐resolution, while venting the system at programmed intervals to prevent over pressurization. The utility of A‐APES is demonstrated in this study by quantifying the growth rate and phases of a biomass‐degrading anaerobic gut fungus, which cannot be otherwise measured via conventional techniques due to its association with particulate substrates. Given the utility of the A‐APES approach, we provide a complete construction guide to fabricate the device, which is three times less expensive compared to existing commercial alternatives