Variational optimization of probability measure spaces resolves the chain store paradox

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.Comment: 11 pages, 5 figures. Replaced for minor notational correctio

Isomorphic Strategy Spaces in Game Theory

This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same strategic situation. In particular, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the dimensionality and volume of the underlying probability parameter spaces. These differences arise as probability theory employs structure preserving isomorphic mappings when constructing strategy spaces to analyze games. In contrast, game theory uses weaker mappings which change some of the properties of the underlying probability distributions within the mixed strategy space. Here, we explore how using strong isomorphic mappings to define game strategy spaces can alter rational outcomes in simple games . Specific example games considered are the chain store paradox, the trust game, the ultimatum game, the public goods game, the centipede game, and the iterated prisoner's dilemma. In general, our approach provides rational outcomes which are consistent with observed human play and might thereby resolve some of the paradoxes of game theory.Comment: 160 pages, 43 figure

Continuous Fuzzy Measurement of Energy for a Two-Level System

A continuous measurement of energy which is sharp (perfect) leads to the quantum Zeno effect (freezing of the state). Only if the quantum measurement is fuzzy, continuous monitoring gives a readout E(t) from which information about the dynamical development of the state vector of the system may be obtained in certain cases. This is studied in detail. Fuzziness is thereby introduced with the help of restricted path integrals equivalent to non-Hermitian Hamiltonians. For an otherwise undisturbed multilevel system it is shown that this measurement represents a model of decoherence. If it lasts long enough, the measurement readout discriminates between the energy levels and the von Neumann state reduction is obtained. For a two-level system under resonance influence (which undergoes in absence of measurement Rabi oscillations between the levels) different regimes of measurement are specified depending on its duration and fuzziness: 1) the Zeno regime where the measurement results in a freezing of the transitions between the levels and 2) the Rabi regime when the transitions maintain. It is shown that in the Rabi regime at the border to the Zeno regime a correlation exists between the time dependent measurement readout and the modified Rabi oscillations of the state of the measured system. Possible realizations of continuous fuzzy measurements of energy are sketched.Comment: 29 pages in LATEX, 1 figure in EPS, to be published in Physical Review

A novel cultivation-based approach for understanding the Miscellaneous Crenarchaeotic Group (MCG) Archaea from sedimentary ecosystems

The uncultured miscellaneous crenarchaeotic group (MCG) archaea comprise one of the most abundant microbial groups in the Earth's subsurface environment. However, very little information is available regarding the lifestyle, physiology, and factors controlling the distribution of members of this group. We established a novel method using both cultivation and molecular techniques, including a pre-PCR propidium monoazide treatment, to investigate viable members of the MCG in vitro. Enrichment cultures prepared from estuarine sediment were provided with one of a variety of carbon substrates or cultivation conditions and incubated for 3 weeks. Compared with the samples from time zero, there was an order-of-magnitude increase in the number of MCG 16S rRNA genes in almost all cultures, indicating that MCG archaea are amenable to in vitro cultivation. None of the tested substrates or conditions significantly stimulated growth of MCG archaea more than the basal medium alone; however, glycerol (0.02%) had a significantly inhibitory effect (P < 0.05). Diversity analysis of populations resulting from four culture treatments (basal medium, addition of amino acids, H2-CO2 as the gas phase, or initial aerobic conditions) revealed that the majority of viable MCG archaea were affiliated with the MCG-8 and MCG-4 clusters. There were no significant differences in MCG diversity between these treatments, also indicating that some members of MCG-4 and MCG-8 are tolerant of initially oxic conditions. The methods outlined here will be useful for further investigation of MCG archaea and comparison of substrates and cultivation conditions that influence their growth in vitro

Extensive microbial and functional diversity within the chicken cecal microbiome

Chickens are major source of food and protein worldwide. Feed conversion and the health of chickens relies on the largely unexplored complex microbial community that inhabits the chicken gut, including the ceca. We have carried out deep microbial community profiling of the microbiota in twenty cecal samples via 16S rRNA gene sequences and an in-depth metagenomics analysis of a single cecal microbiota. We recovered 699 phylotypes, over half of which appear to represent previously unknown species. We obtained 648,251 environmental gene tags (EGTs), the majority of which represent new species. These were binned into over two-dozen draft genomes, which included Campylobacter jejuni and Helicobacter pullorum. We found numerous polysaccharide- and oligosaccharide-degrading enzymes encoding within the metagenome, some of which appeared to be part of polysaccharide utilization systems with genetic evidence for the co-ordination of polysaccharide degradation with sugar transport and utilization. The cecal metagenome encodes several fermentation pathways leading to the production of short-chain fatty acids, including some with novel features. We found a dozen uptake hydrogenases encoded in the metagenome and speculate that these provide major hydrogen sinks within this microbial community and might explain the high abundance of several genera within this microbiome, including Campylobacter, Helicobacter and Megamonas

The evolution of controlled multitasked gene networks: The role of introns and other noncoding RNAs in the development of complex organisms

Eukaryotic phenotypic diversity arises from multitasking of a core proteome of limited size. Multitasking is routine in computers, as well as in other sophisticated information systems, and requires multiple inputs and outputs to control and integrate network activity. Higher eukaryotes have a mosaic gene structure with a dual output, mRNA (protein-coding) sequences and introns, which are released from the pre-mRNA by posttranscriptional processing. Introns have been enormously successful as a class of sequences and comprise up to 95% of the primary transcripts of protein-coding genes in mammals. In addition, many other transcripts (perhaps more than half) do not encode proteins at all, but appear both to be developmentally regulated and to have genetic function. We suggest that these RNAs (eRNAs) have evolved to function as endogenous network control molecules which enable direct gene-gene communication and multitasking of eukaryotic genomes. Analysis of a range of complex genetic phenomena in which RNA is involved or implicated, including co-suppression, transgene silencing, RNA interference, imprinting, methylation, and transvection, suggests that a higher-order regulatory system based on RNA signals operates in the higher eukaryotes and involves chromatin remodeling as well as other RNA-DNA, RNA-RNA, and RNA-protein interactions. The evolution of densely connected gene networks would be expected to result in a relatively stable core proteome due to the multiple reuse of components, implying,that cellular differentiation and phenotypic variation in the higher eukaryotes results primarily from variation in the control architecture. Thus, network integration and multitasking using trans-acting RNA molecules produced in parallel with protein-coding sequences may underpin both the evolution of developmentally sophisticated multicellular organisms and the rapid expansion of phenotypic complexity into uncontested environments such as those initiated in the Cambrian radiation and those seen after major extinction events