On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case

The takeoff point for this letter is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this literature dealing with Kelly Betting. With this as the high-level motivation, we study the potential for use of nonlinear control in this framework. To this end, we consider a “demonstration case” which is one of the simplest scenarios encountered in this line of research: repeated flips of a biased coin with probability of heads p , and even-money payoff on each flip. First, we formulate a new robust nonlinear control problem which we believe is both simple to understand and apropos for dealing with concerns about distributional robustness; i.e., instead of assuming that p is perfectly known as in the case of the classical Kelly formulation, we begin with a bounding set P⊆[0,1] for this probability. Then, we provide a theorem, our main result, which gives a closed-form description of the optimal robust nonlinear controller and a corollary which establishes that it robustly outperforms linear controllers such as those found in the literature. A second, less significant, contribution of this letter bears upon the computability of our solution. For an n-flip game, whereas an admissible controller has 2n−1 parameters, at the optimum only O( n2 ) of them turn out to be distinct. Finally, it is noted that the initial assumptions on payoffs and the use of the uniform distribution on p are made mainly for simplicity of the exposition and compliance with length requirements for a Letter. Accordingly, this letter also includes a new Section with a discussion indicating how these assumptions can be relaxed

Preliminary Investigation Into The Benefits From Investments In Environmental Research: Case Studies on Water Clarity/Quality and The Biological Management of Possums

MoRST is performing an evaluation of the funds invested in environmental research. The two case studies discussed in this paper contribute to the ongoing decision-making about this investment. Substantial funds have been invested in both research programmes identified. Because the main benefits associated with research output are environmental, they are difficult to value monetarily. Preliminary analysis suggests that at a discount rate of 6%, annual future benefit flows of $7 -$10 million will justify the water quality/clarity research. The expenditure on possum biocontrol will be justified if the research generates an annual future benefit flow of $20 million.Cost benefit analysis, returns to research, environmental research, Community/Rural/Urban Development, Environmental Economics and Policy, Land Economics/Use, Resource /Energy Economics and Policy,

After Libra, the e-CNY and COVID-19: the new world of money and payments

Facebook’s stable cryptocurrency, COVID-19, and China’s central bank digital currency, the e-CNY, have caused a reorientation of monetary and payment systems around the world. Ross P. Buckley, Douglas W. Arner, Dirk A. Zetzsche, and Anton Didenko envisage three emerging design choices for these systems, reflected in centralised, decentralised and hybrid models. They predict that the advent of national monetary competition through major economies’ sovereign digital currencies will be one of the defining developments of the next decade

Allozyme variation and genetic relationships among species in the Carex willdenowii complex (Cyperaceae)

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142149/1/ajb20546.pd

Optimized unconventional superconductivity in a molecular Jahn-Teller metal

Understanding the relationship between the superconducting, the neighboring insulating, and the normal metallic state above Tc is a major challenge for all unconventional superconductors. The molecular A3C60 fulleride superconductors have a parent antiferromagnetic insulator in common with the atom-based cuprates, but here, the C603– electronic structure controls the geometry and spin state of the structural building unit via the on-molecule Jahn-Teller effect. We identify the Jahn-Teller metal as a fluctuating microscopically heterogeneous coexistence of both localized Jahn-Teller–active and itinerant electrons that connects the insulating and superconducting states of fullerides. The balance between these molecular and extended lattice features of the electrons at the Fermi level gives a dome-shaped variation of Tc with interfulleride separation, demonstrating molecular electronic structure control of superconductivity

New Constraints on Cosmic Reionization from the 2012 Hubble Ultra Deep Field Campaign

Understanding cosmic reionization requires the identification and characterization of early sources of hydrogen-ionizing photons. The 2012 Hubble Ultra Deep Field (UDF12) campaign has acquired the deepest infrared images with the Wide Field Camera 3 aboard Hubble Space Telescope and, for the first time, systematically explored the galaxy population deep into the era when cosmic microwave background (CMB) data indicates reionization was underway. The UDF12 campaign thus provides the best constraints to date on the abundance, luminosity distribution, and spectral properties of early star-forming galaxies. We synthesize the new UDF12 results with the most recent constraints from CMB observations to infer redshift-dependent ultraviolet (UV) luminosity densities, reionization histories, and electron scattering optical depth evolution consistent with the available data. Under reasonable assumptions about the escape fraction of hydrogen ionizing photons and the intergalactic medium clumping factor, we find that to fully reionize the universe by redshift z~6 the population of star-forming galaxies at redshifts z~7-9 likely must extend in luminosity below the UDF12 limits to absolute UV magnitudes of M_UV\sim -13 or fainter. Moreover, low levels of star formation extending to redshifts z~15-25, as suggested by the normal UV colors of z\simeq7-8 galaxies and the smooth decline in abundance with redshift observed by UDF12 to z\simeq10, are additionally likely required to reproduce the optical depth to electron scattering inferred from CMB observations.Comment: Version accepted by ApJ (originally submitted Jan 5, 2013). The UDF12 website can be found at http://udf12.arizona.ed

Simple high-cell density fed-batch technique for high-level recombinant protein production with Pichia pastoris: Application to intracellular production of Hepatitis B surface antigen

<p>Abstract</p> <p>Background</p> <p>Hepatitis B is a serious global public health concern. Though a safe and efficacious recombinant vaccine is available, its use in several resource-poor countries is limited by cost. We have investigated the production of Hepatitis B virus surface antigen (HBsAg) using the yeast <it>Pichia pastoris </it>GS115 by inserting the <it>HBsAg </it>gene into the alcohol oxidase 1 locus.</p> <p>Results</p> <p>Large-scale production was optimized by developing a simple fed-batch process leading to enhanced product titers. Cells were first grown rapidly to high-cell density in a batch process using a simple defined medium with low salt and high glycerol concentrations. Induction of recombinant product synthesis was carried out using rather drastic conditions, namely through the addition of methanol to a final concentration of 6 g L^-1. This methanol concentration was kept constant for the remainder of the cultivation through continuous methanol feeding based on the <it>on-line </it>signal of a flame ionization detector employed as methanol analyzer in the off-gas stream. Using this robust feeding protocol, maximum concentrations of ~7 grams HBsAg per liter culture broth were obtained. The amount of soluble HBsAg, competent for assembly into characteristic virus-like particles (VLPs), an attribute critical to its immunogenicity and efficacy as a hepatitis B vaccine, reached 2.3 grams per liter of culture broth.</p> <p>Conclusion</p> <p>In comparison to the highest yields reported so far, our simple cultivation process resulted in an ~7 fold enhancement in total HBsAg production with more than 30% of soluble protein competent for assembly into VLPs. This work opens up the possibility of significantly reducing the cost of vaccine production with implications for expanding hepatitis B vaccination in resource-poor countries.</p