Essential Tools of Linear Algebra for Calculating Nuclear Spin Dynamics of Chemically Exchanging Systems

In this work, we describe essential tools of linear algebra necessary for calculating the effect of chemical exchange on spin dynamics and polarization transfer in various nuclear magnetic resonance (NMR) experiments. We show how to construct Hamiltonian, relaxation, and chemical exchange superoperators in the Liouville space, as well as demonstrate corresponding code in Python. Examples of applying the code are given for problems involving chemical exchange between NH3 and NH4+ at zero and high magnetic field and polarization transfer from parahydrogen relevant in SABRE (signal amplification by reversible exchange) at low magnetic field (0-20 mT). The presented methodology finds utility for describing the effect of chemical exchange on NMR spectra and can be extended further by taking into account non-linearities in the master equation

Optimal routing on complex networks

We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing the maximum node betweenness with as little path lengthening as possible, thus being useful in cases when networks are jamming due to queuing overload. By using the resulting routing table, a network can sustain significantly higher traffic without jamming than in the case of traditional shortest path routing.Comment: 4 pages, 5 figure

Is type 2 diabetes really resolved after laparoscopic sleeve gastrectomy? Glucose variability studied by continuous glucose monitoring

The study was carried out on type 2 diabetic obese patients who underwent laparoscopic sleeve gastrectomy (LSG). Patients underwent regular glycemic controls throughout 3 years and all patients were defined cured from diabetes according to conventional criteria defined as normalization of fasting glucose levels and glycated hemoglobin in absence of antidiabetic therapy. After 3 years of follow-up, Continuous Glucose Monitoring (CGM) was performed in each patient to better clarify the remission of diabetes. In this study, we found that the diabetes resolution after LSG occurred in 40% of patients; in the other 60%, even if they showed a normal fasting glycemia and A1c, patients spent a lot of time in hyperglycemia. During the oral glucose tolerance test (OGTT), we found that 2 h postload glucose determinations revealed overt diabetes only in a small group of patients and might be insufficient to exclude the diagnosis of diabetes in the other patients who spent a lot of time in hyperglycemia, even if they showed a normal glycemia (<140 mg/dL) at 120 minutes OGTT. These interesting data could help clinicians to better individualize patients in which diabetes is not resolved and who could need more attention in order to prevent chronic complications of diabetes