Since 1968, when the Golomb–Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb–Welch conjecture. Further, new results on Golomb–Welch con...

The Math Factor podcast posed the problem of finding the smallest number of inch marks on a 12 inch ruler so that one could still measure any integer length from 1 to 12. One needs only four additional marks besides 0 and 12; for example 1, 4, 7, 10 works. This entertaining problem lead to others during the next few minutes (you can listen at mathfactor.uark.edu/2005/10) and inspired us to look...

In the early 1950s, Golay studied binary sequence pairs whose autocorrelation properties are ideal for use in the design of multislit spectrometers. He found examples for some small lengths, but, unable to find more, he suggested that perhaps further examples do not exist and turned his attention to an alternative solution to the design problem (involving what are now called Golay complementary...

The Golomb Ruler problem consists in finding n integers such that all possible differences are distinct and such that the largest difference is minimum. We review three lower bounds based on linear programming that have been proposed in the literature for this problem, and propose a new one. We then show that these 4 lower bounds are equal. Finally we discuss some computational experience aimin...

We performed whole-brain fMRI to explore the neural mechanisms that contribute to the ability to manipulate an object with complex dynamics. Subjects grasped a weighted flexible ruler and balanced it in an unstable equilibrium position as an archetype of grasping an object with complex dynamics. This was contrasted with squeezing a soft foam ball as an archetype of grasping an object with simpl...

The RULER Approach to Social and Emotional Learning ("RULER") is designed to improve the quality of classroom interactions through professional development and classroom curricula that infuse emotional literacy instruction into teaching-learning interactions. Its theory of change specifies that RULER first shifts the emotional qualities of classrooms, which are then followed, over time, by impr...

Absolute protein quantification using mass spectrometry (MS)-based proteomics delivers protein concentrations or copy numbers per cell. Existing methodologies typically require a combination of isotope-labeled spike-in references, cell counting, and protein concentration measurements. Here we present a novel method that delivers similar quantitative results directly from deep eukaryotic proteom...

The aim of this pilot study was to compare interrater and intrarater reliability and to provide analysis of difference of common measurement tools used in podiatry. The tools used to measure the surface area in this study were ruler, tracings and photographic methods. Ten volunteers participated in the study. The surface area for the tracing was determined by counting the squares on graph paper...

Optical rulers have served as a key tool for scientists from different disciplines to address a wide range of biological activity. Since the optical window of state of the art FRET rulers is limited to a 10 nm distance, developing long range optical rulers is very important to monitor real life biological processes. Driven by this need, the current manuscript reports for the first time the desi...