The 99th Fibonacci Identity

We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left open in the book Proofs That Really Count [1], and generalize these to Gibonacci sequences Gn that satisfy the Fibonacci recurrence, but with arbitrary real initial conditions. We offer several new identities as well. [1] A. T. Benjamin and J. J. Quinn, Proofs That Really Count: The Art of Combinatorial Proof, The Dolciani Mathematical Expositions, 27, Mathematical Association of America, Washington, DC, 200

Idea or Prime Opportunity? A Framework for Evaluating Business Ideas for New and Small Ventures

 Entrepreneurs and entrepreneurship educators recognize that only a small percentage of venture ideas actually represent viable business opportunities. This paper addresses the important issue of opportunity recognition using a framework designed with a mnemonic structure for easy recall and based on the extant literature on opportunity recognition. The framework prompts users to examine Product/service, Resource, Individual, Market, and Economic start-up issues. Thus, the PRIME analysis is a heuristic designed for initial opportunity evaluation of a business concept prior to preparing a full-blown business plan. We discuss and apply this framework, demonstrating its effectiveness in the classroom and in practice.

Trajectories of change in well-being during cognitive-behavior therapies for anxiety disorders: quantifying the impact and covariation with improvements in anxiety

Despite substantial evidence supporting the efficacy of cognitive behavioral therapy for reducing many forms of mental illness, less is known about whether CBT also promotes mental health or well being. We will discuss results of a recent study (Gallagher et al., 2019) examining changes in well being d uring different CBT treatments for anxiety disorders and how these changes relate to anxiety. In that study, 223 adults (55.6% female, Mage=31.1 yrs) were randomized to one of five CBT protocols for anxiety disorders at an outpatient clinic. Effect sizes w ere calculated to examine the timing and magnitude of changes in well being as a result of CBT. Further, parallel process latent growth curve models were conducted to examine the extent to which trajectories of changes in well being correlated with the tra jectories of change in both clinician rated and self reported anxiety during active treatment. Results indicated that there were moderate to large increases in overall well being and the three components of subjective, psychological, and social well being, mainly during the second half of CBT, and these increases were maintained at a 6 month follow up. Further, trajectories of change in well being across treatment were strongly correlated with trajectories of change in clinician rated and self reported anxi ety. Together, these findings suggest that different CBT protocols for anxiety consistently produce robust and lasting changes in different domains of positive mental health and increases in well being are strongly linked to changes in anxiety during treatment.Published versio

Direct patterning of gold nanoparticles using flexographic printing for biosensing applications

In this paper, we have presented the use of flexographic printing techniques in the selective patterning of gold nanoparticles (AuNPs) onto a substrate. Highly uniform coverage of AuNPs was selectively patterned on the substrate surface, which was subsequently used in the development of a glucose sensor. These AuNPs provide a biocompatible site for the attachment of enzymes and offer high sensitivity in the detection of glucose due to their large surface to volume ratio. The average size of the printed AuNPs is less than 60 nm. Glucose sensing tests were performed using printed carbon-AuNP electrodes functionalized with glucose oxidase (GOx). The results showed a high sensitivity of 5.52 μA mM−1 cm−2 with a detection limit of 26 μM. We have demonstrated the fabrication of AuNP-based biosensors using flexographic printing, which is ideal for low-cost, high-volume production of the devices

Analysis of Antibody and Cytokine Markers for Leprosy Nerve Damage and Reactions in the INFIR Cohort in India

Leprosy is one of the oldest known diseases. In spite of the established fact that it is least infectious and a completely curable disease, the social stigma associated with it still lingers in many countries and remains a major obstacle to self reporting and early treatment. The nerve damage that occurs in leprosy is the most serious aspect of this disease as nerve damage leads to progressive impairment and disability. It is important to identify markers of nerve damage so that preventive measures can be taken. This prospective cohort study was designed to look at the potential association of some serological markers with reactions and nerve function impairment. Three hundred and three newly diagnosed patients from north India were recruited for this study. The study attempts to reflect a model of nerve damage initiated by mycobacterial antigens and maintained by ongoing inflammation through cytokines such as Tumour Necrosis Factor alpha and perhaps extended by antibodies against nerve components