Analysis of the Penney-Ante Game Using Difference Equations: Development of an Optimal and a Mixed-Strategies Protocol

Penney-Ante is a well known two-player (Player I and Player II) game based on an information paradox. We present a new approach, using difference-equations, to analyzing the outcome for each player. One strategy yields a winning outcome of 75% for Player II, the player playing second. The approach also permits investigation of non-optimal strategies, and demonstrates how mixing of such strategies can be used to tune the winning edge of either player. We generalize the analysis to accommodate the possibility of a biased coin

iPads in the Science Laboratory: Experience in Designing and Implementing a Paperless Chemistry Laboratory Course

In the fall of 2012, 20 General Chemistry Honors students at the University of New Haven were issued the new iPad 3 to incorporate these devices both in the classroom and the laboratory. This paper will focus on the integration of the iPad into the laboratory curriculum while creating a paperless experience, an environment where no paper would enter or be used for the laboratory over the course of the year. Specific apps were chosen that would allow for an easy transition of course materials into an electronic format. After a transition period for the students and instructor, the overall experience has been a positive one and can easily be implemented into any teaching laboratory

Computational Models of Chemical Systems Inspired by Braess’ Paradox

Systems chemistry is a new discipline which investigates the interactions within a network of chemical reactions. We have studied several computational models of chemical systems inspired by mathematical paradoxes and have found that even simple systems may behave in a counterintuitive, non-linear manner depending upon various conditions. In the present study, we modeled a set of reactions inspired by one such paradox, Braess’ paradox, an interesting phenomenon whereby the introduction of additional capacity (e.g. pathways) in some simple network systems can lead to an unexpected reduction in the overall flow rate of “traffic” through the system. We devised several chemical systems that behaved in this counterintuitive manner; the overall rate of product formation was diminished when an additional pathway was introduced and, conversely, there was an enhancement of product formation when the same interconnecting pathway was removed. We found that, unlike a traffic model, the chemical model needed to include reversible pathways in order to mimic “congestion”—a condition necessary to produce Braess-like behavior. The model was investigated numerically, but a full analytical solution is also included. We propose that this intriguing situation may have interesting implications in chemistry, biochemistry and chemical engineering

Kinetic Models of the Prebiotic Replication of dsRNA under Thermal Cycling Conditions

We present computational models for the replication of double stranded RNA (dsRNA) or related macromolecules under thermal cycling conditions that would reflect prebiotic (i.e. non-enzymatic) environments. Two models of the replication of dsRNA are represented as multi-step chemical systems. The objective of this investigation was to better understand the kinetic features of such chemical systems. It is shown that thermal cycling in a chemical system is advantageous (relative to a fixed temperature) if there are two competing reactions, one favored at high temperature and one favored at low temperature. For the prebiotic replication of dsRNA, a high temperature favors formation of the two single stranded RNA (ssRNA) templates and a presumptive catalysis or catalytic surface is active at low temperature at which the ssRNA template is copied. Our models may facilitate understanding possible prebiotic conditions for the replication of dsRNA

Computational Models of Thermal Cycling in Chemical Systems

Computational models of chemical systems provide clues to counterintuitive interactions and insights for new applications. We have been investigating models of chemical reaction systems under forced, thermal cycling conditions and have found that some hypothetical processes generate higher yields under thermal cycling than under single, fixed temperature conditions. A simple kinetic model of an actual process, the two-temperature polymerase chain reaction that replicates DNA, is used to simulate the important features of a chemical system operating under thermal cycling. This model provides insights into the design of other chemical systems that may have important applications in chemistry, biochemistry and chemical engineering

Systems Chemistry and Parrondo’s Paradox: Computational Models of Thermal Cycling

A mathematical concept known as Parrondo’s paradox motivated the development of several novel computational models of chemical systems in which thermal cycling was explored. In these kinetics systems we compared the rates of formation of product under cycling temperature and steady-sate conditions. We found that a greater concentration of product was predicted under oscillating temperature conditions. Our computational models of thermal cycling suggest new applications in chemical and chemical engineering systems

A Hybrid First Year Science Course For Engineering Students – Integrating Biology With Chemistry

Biology is playing an increasingly important role in many engineering fields. With the typical engineering program already having a high credit hour requirement, the question becomes, how to best integrate biology concepts into a packed engineering curriculum. A typical biology course is not likely to introduce the important concepts of biology to engineering students. The solution here is to develop a hybrid course that integrates chemistry and biology. In the course, Chemistry with Applications to Biosystems, the concept is to develop a course that integrally links important concepts of chemistry and biology. The course focuses on the areas of biology most relevant to engineers: the structure and function of biologically important molecules, and concepts of biosystems (cell proliferation, immune and nervous systems and metabolism). A special topics thread has been included to weave current events into the course. During the most recent offering the focus was on various aspects of bird flu. This is a required course for Chemical, Civil and General Engineering students and is an elective taken by a large fraction of Mechanical Engineering students as part of the Multidisciplinary Engineering Foundation Spiral Curriculum. The course is typically taken during the second semester in place of a second general chemistry course. The course has been structured to provide the background needed for subsequent study of organic chemistry and physical chemistry. The introduction to concepts of biology is also structured to provide the necessary foundation for incorporation of biological applications in upper level engineering courses such as mass transfer. The course includes a laboratory component incorporating experiments from biology and environmental engineering concepts with classical general chemistry. Approximately one half of the experiments are common with a typical second semester general chemistry course. The remaining experiments include protein assay, enzyme kinetics, acid base behavior of amino acids and biochemical oxygen demand. The laboratory component also places a heavy emphasis on data analysis, uncertainty analysis and applications of statistics in experimentation. This paper will detail the development and delivery of Chemistry with Applications to Biosystems. Comparative data will be presented to illustrate the performance of students in subsequent course work, particularly organic chemistry

Analysis of a Chemical Model System Leading to Chiral Symmetry Breaking: Implications for the Evolution of Homochirality

Explaining the evolution of a predominantly homochiral environment on the early Earth remains an outstanding challenge in chemistry. We explore here the mathematical features of a simple chemical model system that simulates chiral symmetry breaking and amplification towards homochirality. The model simulates the reaction of a prochiral molecule to yield enantiomers via interaction with an achiral surface. Kinetically, the reactions and rate constants are chosen so as to treat the two enantiomeric forms symmetrically. The system, however, incorporates a mechanism whereby a random event might trigger chiral symmetry breaking and the formation of a dominant enantiomer; the non-linear dynamics of the chemical system are such that small perturbations may be amplified to near homochirality. Mathematical analysis of the behavior of the chemical system is verified by both deterministic and stochastic numerical simulations. Kinetic description of the model system will facilitate exploration of experimental validation. Our model system also supports the notion that one dominant enantiomeric structure might be a template for other critical molecules

Multiple-Choice Testing Using Immediate Feedback-Assessment Technique (IF AT®) Forms: Second-Chance Guessing vs. Second-Chance Learning?

Multiple choice testing is a common but often ineffective method for evaluating learning. A newer approach, however, using Immediate Feedback Assessment Technique (IF AT®, Epstein Educational Enterprise, Inc.) forms, offers several advantages. In particular, a student learns immediately if his or her answer is correct and, in the case of an incorrect answer, has an opportunity to provide a second response and receive partial credit for a correct second attempt. For a multiple choice question with five possible answers, the IF AT® form covers spaces labeled A through E with a thin opaque film; when the film is scratched away, a star indicates the correct answer. This study was conducted in order to assess learning after an initial incorrect answer. Based on random chance, students should have mathematically a 25% chance of guessing a correct second answer (i.e. 1 of 4 remaining answers on the IF AT® form). Analysis of second responses for 8775 questions on IF AT® forms in 22 classes over 3 years showed that the percent of correct second answers was 44.9%, significantly higher than one might expect from random guessing. This indicates that students learned from an incorrect answer and, possibly by re-reading the problem, were able to demonstrate some level of mastery of the material. This data leads us to conclude that IF AT® forms are useful assessment tools