Find, Process, and Share: An Optimal Control in the Vidale-Wolfe Marketing Model

The Vidale-Wolfe marketing model is a first-order, linear, non-homogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students chose it for an exploratory project that we designed in order to help students acquire the ability to interpret and communicate mathematical results. In addition to describing the project in this work, we discuss the Vidale-Wolfe model and show how it can lead one to use Green\u27s theorem in a real situation

Facing the Pandemic Together: Forming a Collaborative Research Group

This is an account of how a reading and writing project in an introductory differential equations course was transitioned to a professor-student research group collaborative project, in response to the global COVID-19 pandemic. Adapting on the fly to the ever-evolving pandemic, we collected data, estimated parameters in our models, and computed numerical solutions to SIR-based systems of differential equations. This is a description of what we did and how we found comfort in the project in this time of great uncertainty. The collaboration yielded successes and more questions than we had answers for, but the situation provided an opportunity of a lifetime for my students to engage in a real-world developing situation

Responsible aquaculture development for the next millennium

With the world population doubling in size from 3 to 6 billion people from 1960 to 1999 and currently growing at 1.33% per year (or an annual net addition of 78 million people), and expected to reach 7.3 to 10.7 billion by 2050 (with 8.9 billion considered most likely), there are growing doubts as to the long term sustainability of many traditional agricultural food production systems in being able to meet the increasing global demand for food. Nowhere is this more critical than within many of the world s developing countries, and in particular within those Low-income Food-deficit countries (LIFDC ; currently representing over 62% of the world s population), which are net importers of food and lack sufficient earnings to purchase food to cover their basic dietary needs. Of the multitude of agricultural food production systems, aquaculture is widely viewed as being an important potential candidate capable of contributing to reductions in the shortfall in the terrestrial food basket. Aquaculture, the farming of aquatic plants and animals, has been the fastest growing food production sector for over a decade. Total global production from aquaculture more than tripled from 10 million metric tons (mmt) in 1984 to over 36 mmt in 1997, and production grew at an average compound rate of 1 l% per year since 1984. In contrast to traditional livestock food production systems, the bulk of global aquaculture is realised within developing countries (89.6% total) and LIFDCs (80.6% total). Despite its good prospects and apparent potential for continued growth, the aquaculture sector has not been without its problems and critics. In particular, there have been concerns raised related to deficiencies in existing aquaculture legislation and planning methods, the use of certain farming practices, issues of resource use efficiency, disease treatment and control, environmental degradation, social welfare, and employment opportunities, etc. Although the majority of these are not unique to the aquaculture sector, it is imperative that these issues be addressed and resolved if the sector is to emerge into a major global food production sector in the next millennium. In addition, the present paper reviews the origins and salient features of the FAO Code of Conduct for Responsible Fisheries (CCRF), and in particular of Article 9 of CCRF concerning aquaculture development. An overview is also presented of ongoing and planned initiatives concerning the implementation of the code. In particular, the paper attempts to consider the existing socioeconomic conditions of the majority of aquaculture producing countries within the Asian region, and the real basic need of identifying affordable and practical solutions to aid the development of the sector. Particular emphasis is placed on the need of government to provide an enabling economic and legislative environment and umbrella for the sustainable and responsible development of the sector, and the need for increased collaboration between the private and public sector organizations, and government engaged in all stages of the aquaculture development process.The first author would like to acknowledge the support of the Tropical Aquaculture Feeds and Culture Technology Development Project II: Development of Shrimp Feeds, USDA-ARS Grant Agreement No. 59-5320-7-989. Both authors are most grateful for the kind invitation by the SEAFDEC Aquaculture Department to join the 1999 ADSEA Seminar-Workshop

Spectral approach to linear programming bounds on codes

We give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte's linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal polynomials. The examples of the method considered in the paper include binary codes, binary constant-weight codes, spherical codes, and codes in the projective spaces.Comment: 11 pages, submitte

Novel DNA methylation profiles associated with key gene regulation and transcription pathways in blood and placenta of growth-restricted neonates

BB/H012494/1/ Biotechnology and Biological Sciences Research Counci

Understanding Mechanical Response of Elastomeric Graphene Networks

Ultra-light porous networks based on nano-carbon materials (such as graphene or carbon nanotubes) have attracted increasing interest owing to their applications in wide fields from bioengineering to electrochemical devices. However, it is often difficult to translate the properties of nanomaterials to bulk three-dimensional networks with a control of their mechanical properties. In this work, we constructed elastomeric graphene porous networks with well-defined structures by freeze casting and thermal reduction, and investigated systematically the effect of key microstructural features. The porous networks made of large reduced graphene oxide flakes (>20 μm) are superelastic and exhibit high energy absorption, showing much enhanced mechanical properties than those with small flakes (<2 μm). A better restoration of the graphitic nature also has a considerable effect. In comparison, microstructural differences, such as the foam architecture or the cell size have smaller or negligible effect on the mechanical response. The recoverability and energy adsorption depend on density with the latter exhibiting a minimum due to the interplay between wall fracture and friction during deformation. These findings suggest that an improvement in the mechanical properties of porous graphene networks significantly depend on the engineering of the graphene flake that controls the property of the cell walls

A Complementary Marriage of Perspectives: Understanding Organizational Social Context Using Mixed Methods

Background: Organizational factors impact the delivery of mental health services in community settings. Mixed-methods analytic approaches have been recommended, though little research within implementation science has explicitly compared inductive and deductive perspectives to understand their relative value in understanding the same constructs. The purpose of our study is to use two different paradigmatic approaches to deepen our understanding of organizational social context. We accomplish this by using a mixed-methods approach in an investigation of organizational social context in community mental health clinics. Methods: Nineteen agencies, representing 23 sites, participated. Enrolled participants included 130 therapists, 36 supervisors, and 22 executive administrators. Quantitative data was obtained via the Organizational Social Context (OSC) measure. Qualitative data, comprised of direct observation with spot sampling generated from agency visits, was coded using content analysis and grounded theory. The present study examined elements of organizational social context that would have been missed if only quantitative data had been obtained and utilized mixed methods to investigate if stratifying observations based on quantitative ratings from the OSC resulted in the emergence of differential themes. Results: Four of the six OSC constructs were commonly observed in field observations (i.e., proficiency, rigidity, functionality, stress), while the remaining two constructs were not frequently observed (i.e., resistance, engagement). Constructs emerged related to organizational social context that may have been missed if only quantitative measurement was employed, including those around the physical environment, commentary about evidence-based practice initiatives, leadership, cultural diversity, distrust, and affect. Stratifying agencies by “best,” “average,” and “worst” organizational social context impacted interpretation for three constructs (affect, stress, and leadership). Conclusions: Results support the additive value of integrating inductive and deductive perspectives in implementation science research. This synthesis of approaches facilitated a more comprehensive understanding and interpretation of the findings than would have been possible if either methodology had been employed in isolation