2-factors with k cycles in Hamiltonian graphs

A well known generalisation of Dirac’s theorem states that if a graph G on n ≥ 4k vertices has minimum degree at least n/2 then G contains a 2-factor consisting of exactly k cycles. This is easily seen to be tight in terms of the bound on the minimum degree. However, if one assumes in addition that G is Hamiltonian it has been conjectured that the bound on the minimum degree may be relaxed. This was indeed shown to be true by S´ark¨ozy. In subsequent papers, the minimum degree bound has been improved, most recently to (2/5 + ε)n by DeBiasio, Ferrara, and Morris. On the other hand no lower bounds close to this are known, and all papers on this topic ask whether the minimum degree needs to be linear. We answer this question, by showing that the required minimum degree for large Hamiltonian graphs to have a 2-factor consisting of a fixed number of cycles is sublinear in n

Nearly-linear monotone paths in edge-ordered graphs

How long a monotone path can one always find in any edge-ordering of the complete graph Kn? This appealing question was first asked by Chv´atal and Koml´os in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n 2/3−o(1). In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length n 1−o(1

Nearly-linear monotone paths in edge-ordered graphs

How long a monotone path can one always find in any edge-ordering of the complete graph Kn? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n^2/3−o(1). In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length n^1−o(1)

The Future of Marketing Education is Now: 2018 Annual Fall Conference Proceedings

This paper showcases an approach to learning design in a foundation Marketing course which leveraged the integration of new technologies in an aligned design, to create disruptive innovation in the marketing classroom. Adaptive personalization strategies using a total activity system enabled a digitally supported learning ecosystem with multiple parties co-creating value. Learning analytics layered with adaptive technologies enabled efficient data-based customization to provide personalization of the learning experience. Early results demonstrated the value of integrating new techniques and technologies to guide course design for improved learning outcomes and a better student experience

Influence of antipsychotics on metabolic syndrome risk in patients with schizophrenia

Objective: Many studies so far have shown that antipsychotic therapy may have an effect on the development of metabolic syndrome in patients diagnosed with schizophrenia. Our goal was to determine whether our respondents are at risk for developing metabolic syndrome and who is more predisposed to it. Methods: In a stable phase, 60 patients diagnosed with schizophrenia were equally divided into three groups according to the drug (risperidone, clozapine, and aripiprazole monotherapy). Control group had 20 healthy examinees. Patients were evaluated first using The Positive and Negative Syndrome Scale (PANSS). Prolactin, lipid status, glycemia, insulin, cytokine values (IL-33, TGF-β, and TNF-α) and C-reactive protein (CRP) were measured. Also, Body mass index (BMI), Homeostatic Model Assesment for Insulin Resistance (HOMA index), waist and hip circumference (WHR) and blood pressure (TA) measurement were performed in the study. Results: Patients treated with risperidone compared to healthy control subjects and aripiprazol group of patients had statistically significant difference in prolactin levels. In clozapine group compared to healthy control group values of HDL cholesterol and glucose level were statistically significant different. In aripiprazole group compared to healthy control group value of BMI was statistically significant different. Statistically significant correlations were found in TNF-α with glucose and HOMA index in risperidone treated patients and with BMI in clozapine group of patients; IL-33 with glucose in risperidone and with BMI in clozapine group of patients and TGF-β with glucose in risperidone group, with insulin and HOMA index in clozapine group and statistically significant negative correlation with LDL cholesterol in aripiprazole group of patients. Conclusion: Patients on risperidone and clozapine therapy may be at greater risk of developing metabolic syndrome than patients treated with aripiprazole. Statistically significant difference in concentration of TNF-α and TGF-β was in the group of patients treated with risperidone compared to healthy control group