A variation on bisecting the binomial coefficients

In this paper, we present an algorithm which allows us to search for all the bisections for the binomial coefficients $\{\binom{n}{k} \}_{k=0,...,n}$ and include a table with the results for all $n\le 154$. Connections with previous work on this topic is included. We conjecture that the probability of having only trivial solutions is $5/6$. \end{abstract}Comment: 14 pages, four tables, two figure

Quantal analysis of long-term potentiation of combined neuronal postsynaptic potentials on hippocampal slices in vitro.

10.1007/BF0105247

Street-Fighting Mathematics

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation.In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license

The Association Between Glycosylation of Immunoglobulin G and Hypertension:A Multiple Ethnic Cross-Sectional Study

More than half of all known proteins, and almost all membrane and extra-cellular proteins have oligosaccharide structures or glycans attached to them. Defects in glycosylation pathways are directly involved in at least 30 severe human diseases. A multiple center cross-sectional study (China, Croatia, and Scotland) was carried out to investigate the possible association between hypertension and IgG glycosylation. A hydrophilic interaction chromatography of fluorescently labeled glycans was used to analyze N-glycans attached to IgG in plasma samples from a total of 4757 individuals of Chinese Han, Croatian, and Scottish ethnicity. Five glycans (IgG with digalactosylated glycans) significantly differed in participants with prehypertension or hypertension compared to those with normal blood pressure, while additional 17 glycan traits were only significantly differed in participants with hypertension compared to those of normal blood pressure. These glycans were also significant correlated with systolic blood pressure (SBP) or diastolic blood pressure (DBP). The present study demonstrated for the 1st time an association between hypertension and IgG glycome composition. These findings suggest that the individual variation in N-glycosylation of IgG contributes to pathogenesis of hypertension, presumably via its effect on pro-and/or anti-inflammatory pathways. © Copyright 2016 Wolters Kluwer Health, Inc. All rights reserved