Mathematics

Tension analysis along the retinal surface demonstrates the advantage of meridional buckles over limbal-parallel buckles. A cylindrical sponge generates tensional forces in the retina along the long axis of the buckle and perpendicular to it. The tension perpendicular to the sponge is positive, and the retina and retinal pigment epithelium stretch in that direction. The tension along the long axis is positive (stretching) when the buckle is less than 90 degrees arc length; and negative (compression), greater than 90 degrees for a 5-mm sponge. Consequently, retinal compression folds on the buckles occur for buckles of arc length greater than 90 degrees. These tension forces at right angles to each other explain the development of (1) concave retinal detachment or retinal folds off short limbal-parallel buckles, (2) retinal folds on long limbal-parallel buckles, and (3) fishmouthing of horseshoe tears overlying a limbal-parallel buckle. The buckle increases retinal surface area overlying the buckle. The significance of this is not clear, but it may explain the lessening or disappearance of compression folds on the buckle in time.

We noted that the adjustable fixation device present on some models of the Goldmann-Weekers dark adaptometer has a calibration error that results in a consistent and predictable overestimation of retinal eccentricity. The error occurs because the eye being tested is not in the geometric center of the projection sphere. The true retinal locus may be computed by trigonometric analysis. A conversion table is available for reference.

Mutants of bacteriophage varphiX174 have been isolated that are less dense than wild-type varphiX particles in CsCl. When mutant viral (+) strand DNA and wild-type complementary (-) strand DNA are hybridized, the resulting duplex molecules have single-stranded loops characteristic of wild-type-deletion heteroduplexes. The mutant bacteriophages fail to complement varphiX amber mutants in cistron E. We conclude that the mutant viruses have deleted approximately 7% of the varphiX genome in the region of cistron E.

Mutants of bacteriophage varphiX174 have been isolated that are less dense than wild-type varphiX particles in CsCl. When mutant viral (+) strand DNA and wild-type complementary (-) strand DNA are hybridized, the resulting duplex molecules have single-stranded loops characteristic of wild-type-deletion heteroduplexes. The mutant bacteriophages fail to complement varphiX amber mutants in cistron E. We conclude that the mutant viruses have deleted approximately 7% of the varphiX genome in the region of cistron E.

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.

The question of how an individual bacterial cell grows during its life cycle remains controversial. In 1962 Collins and Richmond derived a very general expression relating the size distributions of newborn, dividing and extant cells in steady-state growth and their growth rate; it represents the most powerful framework currently available for the analysis of bacterial growth kinetics. The Collins-Richmond equation is in effect a statement of the conservation of cell numbers for populations in steady-state exponential growth. It has usually been used to calculate the growth rate from a measured cell size distribution under various assumptions regarding the dividing and newborn cell distributions, but can also be applied in reverse--to compute the theoretical cell size distribution from a specified growth law. This has the advantage that it is not limited to models in which growth rate is a deterministic function of cell size, such as in simple exponential or linear growth, but permits evaluation of far more sophisticated hypotheses. Here we employed this reverse approach to obtain theoretical cell size distributions for two exponential and six linear growth models. The former differ as to whether there exists in each cell a minimal size that does not contribute to growth, the latter as to when the presumptive doubling of the growth rate takes place: in the linear age models, it is taken to occur at a particular cell age, at a fixed time prior to division, or at division itself; in the linear size models, the growth rate is considered to double with a constant probability from cell birth, with a constant probability but only after the cell has reached a minimal size, or after the minimal size has been attained but with a probability that increases linearly with cell size. Each model contains a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. In the present article, the various growth laws are described and rigorous mathematical expressions developed to predict the size distribution of extant cells in steady-state exponential growth; in the following paper, these predictions are tested against high-quality experimental data.

ABSTRACT In this study, we use well-accepted conceptual assessment instruments, initial state data such as the SAT, and our own recently developed instruments designed to measure aptitude in mathematics to develop a machine learning-based predictive model for student performance. Previous analysis found the expected strong correlation between performance in the mathematics and physics courses. The mathematics assessment instruments were designed to provide a means for suggesting corrective measures for students to take to improve performance in mathematics, and it was demonstrated that these measures also have an impact on performance in physics. With the predictive nature of the collected data and the impact of the various corrective measures on final grade established, we use these data to form a predictive model for student performance. By adaptively imputing missing data from previous years, and forming a random forest model, we are able to predict those students who are most at-risk of failing the introductory mathematics and physics courses with acceptable accuracy. This analysis contributes to an integrated evaluation of the current programs, which has led to an assessment-based initiative to offer strategic guidance to incoming students, better placing them for academic and career success in their selected STEM disciplines.

A heretofore overlooked response to Galileo's 1638 'Discorsi' is described by examining two extant copies of the text (one which has received little attention in the historiography, the other apparently unknown) which are heavily annotated. It is first demonstrated that these copies contain annotations made by Seth Ward and Sir Christopher Wren. This article then examines one feature of Ward's and Wren's responses to the 'Discorsi', namely their decision to re-write several of Galileo's geometrical demonstrations into the language of symbolic algebra. It is argued that this type of active reading of period mathematical texts may have been part of the regular scholarly and pedagogical practices of early modern British mathematicians like Ward and Wren. A set of Appendices contains a transcription and translation of the analytical solutions found in these annotated copies.