On the ring of approximation triples attached to a class of extremal real numbers

We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an algebraic point of view by identifying it with the quotient of a polynomial ring over Q. The link between these points of view relies on combinatorial results of independent interest. We apply this theory to estimate the dimension of a certain space of sequences satisfying prescribed growth constrains.Comment: 24 page

Audio-Visual Sentiment Analysis for Learning Emotional Arcs in Movies

Stories can have tremendous power -- not only useful for entertainment, they can activate our interests and mobilize our actions. The degree to which a story resonates with its audience may be in part reflected in the emotional journey it takes the audience upon. In this paper, we use machine learning methods to construct emotional arcs in movies, calculate families of arcs, and demonstrate the ability for certain arcs to predict audience engagement. The system is applied to Hollywood films and high quality shorts found on the web. We begin by using deep convolutional neural networks for audio and visual sentiment analysis. These models are trained on both new and existing large-scale datasets, after which they can be used to compute separate audio and visual emotional arcs. We then crowdsource annotations for 30-second video clips extracted from highs and lows in the arcs in order to assess the micro-level precision of the system, with precision measured in terms of agreement in polarity between the system's predictions and annotators' ratings. These annotations are also used to combine the audio and visual predictions. Next, we look at macro-level characterizations of movies by investigating whether there exist `universal shapes' of emotional arcs. In particular, we develop a clustering approach to discover distinct classes of emotional arcs. Finally, we show on a sample corpus of short web videos that certain emotional arcs are statistically significant predictors of the number of comments a video receives. These results suggest that the emotional arcs learned by our approach successfully represent macroscopic aspects of a video story that drive audience engagement. Such machine understanding could be used to predict audience reactions to video stories, ultimately improving our ability as storytellers to communicate with each other.Comment: Data Mining (ICDM), 2017 IEEE 17th International Conference o

Studies on nucleic acid reassociation kinetics: empirical equations describing DNA reassociation

The rate of appearance of duplex DNA renaturation, measured with single strand specific nuclease, deviates significantly from a second order reaction. Measurements reported in paper I of this series indicate an inhibition in the rate of reassociation of single strand tails on partially reassociated molecules by a factor of at least two. Equations are derived that describe the observed form of reassociation kinetics as measured with hydroxyapatite and with single strand specific nuclease. The free parameter that describes the extent of inhibition of nucleation with single strand tails in these equations has been evaluated by least squares methods and agrees with the experimentally measured value

The Lepidoptera of Fowler Woods State Nature Preserve, Richland County, Ohio.

A survey of the Lepidoptera occurring at Fowler Woods State Nature Preserve in Richland County, Ohio was conducted from 1986 to 1988. Sampling was done by ultraviolet light traps, mercury vapor light and ultraviolet light and collecting sheet, bait traps, sugaring and netting. A total of 419 species and forms was identified and tabulated. It was estimated that the actual number of species at this site is 655. Representative specimens have been deposited in the Insect Reference Collection at the Ohio Agricultural Research and Development Center, The Ohio State Univer- sity, Wooster, Ohio

A Check List of the Lepidoptera of Beaver Creek State Park, Columbiana County, Ohio

Results of a comprehensive survey of Lepidoptera occurring at a 12,334 hectare natural area in Columbiana County. Ohio conducted in 1985 and 1990 is presented. Ten species of skippers, 27 species of butterflies and 597 species and forms of moths were identified and recorded. Euagrotis forbesi, and Spodoptera eridania had not previously been collected in Ohio; and Polia nimbosa and Idia laurenti have been designated as special interest since they are considered rare Ohio residents. The gypsy moth, Lymantria dispar was taken in bait traps and is the first record for that species in the Park. The presence of the gypsy moth, and the possibility of attempted eradication poses a definite threat to the survival of the species mentioned above with the exception of the southern army worm, S. eridama which was undoubtedly a fall migrant

The learning curve in a competitive industry.

We consider the learning curve in an industry with free entry and exit, and price-taking firms. A unique equilibrium exists if the fixed cost is positive. While equilibrium profits are zero, mature firms earn rents on their learning, and, if costs are convex, no firm can profitably enter after the date the industry begins. Under some cost and demand conditions, however, firms may have to exit the market despite their experience gained earlier. Furthermore identical firms facing the same prices may produce different quantities. The market outcome is always socially efficient, even if dictates that firms exit after learning. Finally, actual and optimal industry concentration does not always increase in the intensity of learning.Learning curve; Industry evolution; Perfect competition;