Large circulant graphs of fixed diameter and arbitrary degree

We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case. We present a direct product construction yielding improved bounds for small diameters and introduce a new general technique for “stitching” together circulant graphs which enables us to improve the current best known asymptotic orders for every diameter. As an application, we use our constructions in the directed case to obtain upper bounds on the minimum size of a subset A of a cyclic group of order n such that the k-fold sumset kA is equal to the whole group. We also present a revised table of largest known circulant graphs of small degree and diameter

Resistance training: here's why it's so effective for weight loss. [Blog post]

Weight lifting, also known as resistance training, has been practised for centuries as a way of building muscular strength. Research shows that resistance training, whether done via body weight, resistance bands or machines, dumbbells or free weights, not only helps us build strength, but also improves muscle size and can help counteract age-related muscle loss. More recently it's become popular among those looking to lose weight. While exercises such as running and cycling are indeed effective for reducing body fat, these activities can simultaneously decrease muscle size, leading to weaker muscles and greater perceived weight loss, as muscle is more dense than fat. But unlike endurance exercises, evidence shows resistance training not only has beneficial effects on reducing body fat, it also increases muscle size and strength

Supersets save time in the gym: which may help you reach fitness goals faster. [Blog post]

Resistance training is an increasingly popular way to build strength, lose weight and get in shape. But despite its many benefits, it can also be time consuming – which is why many fitness enthusiasts have started incorporating "supersets" into gym routines. When done properly, supersets have the potential to help you build strength and muscle – all while spending less time in the gym. Sometimes called paired sets, supersets are a form of strength training in which you perform a set of repetitions of usually two exercises, back-to-back with minimal or no rest between them. The exercises should also target opposing muscle groups – namely the agonists (the force-generating muscles) and the antagonists (the muscle that relaxes when the agonist contracts). For example, leg curls (where the hamstrings are the agonists and the quadriceps the antagonists) would typically be followed by leg extensions (where the quadriceps are the agonists and the hamstrings the antagonists) to make up a superset. However, many people perform supersets incorrectly. Many believe supersets to be the same as compound sets, in which two exercises engaging the same muscle group are performed back-to-back. Or they get confused with contrast training, in which two similar exercises are paired to increase power, the first performed with a heavier load, while the second is performed explosively with a lighter load – such as heavy squats followed by vertical jumps. Many also think supersets comprise upper and lower body exercises performed in succession

Dramatic robustness of a multiple delay dispersed interferometer to spectrograph errors: how mixing delays reduces or cancels wavelength drift

We describe demonstrations of remarkable robustness to instrumental noises by using a multiple delay externally dispersed interferometer (EDI) on stellar observations at the Hale telescope. Previous observatory EDI demonstrations used a single delay. The EDI (also called “TEDI”) boosted the 2,700 resolution of the native TripleSpec NIR spectrograph (950-2450 nm) by as much as 10x to 27,000, using 7 overlapping delays up to 3 cm. We observed superb rejection of fixed pattern noises due to bad pixels, since the fringing signal responds only to changes in multiple exposures synchronous to the applied delay dithering. Remarkably, we observed a ~20x reduction of reaction in the output spectrum to PSF shifts of the native spectrograph along the dispersion direction, using our standard processing. This allowed high resolution observations under conditions of severe and irregular PSF drift otherwise not possible without the interferometer. Furthermore, we recently discovered an improved method of weighting and mixing data between pairs of delays that can theoretically further reduce the net reaction to PSF drift to zero. We demonstrate a 350x reduction in reaction to a native PSF shift using a simple simulation. This technique could similarly reduce radial velocity noise for future EDI’s that use two delays overlapped in delay space (or a single delay overlapping the native peak). Finally, we show an extremely high dynamic range EDI measurement of our ThAr lamp compared to a literature ThAr spectrum, observing weak features (~0.001x height of nearest strong line) that occur between the major lines. Because of individuality of each reference lamp, accurate knowledge of its spectrum between the (unfortunately) sparse major lines is important for precision radial velocimetry

Here’s why you don’t need to feel sore after a workout to know it’s worked. [Blog post]

"No pain, no gain" is a commonly used expression when it comes to getting in shape. It may also be why many of us think that you need to feel sore after a workout to know that you've done enough. There are many reasons why your muscles might get sore after a workout. But, contrary to popular belief, you don't necessarily need to feel sore in the hours or days after exercise to know you've had agood workout. Delayed onset muscle soreness – better known as DOMS – is a common experience for many who exercise. Delayed onset muscle soreness (DOMS) is the scientific term to describe the sore and tender feeling our muscles have after a workout. Typically, it happens after we've done particularly strenuous exercise, or if we do exercise we aren't used to. It can happen after any type of exercise, though it's more common after eccentric exercise. These are movements where the muscles resist a load as they're stretched (such as when you're running downhill or descending stairs). The smaller upper-limb muscles (such as your biceps and shoulders) can be more susceptible to DOMS as they may not be accustomed to eccentric exercise

High-resolution broadband spectroscopy using externally dispersed interferometry at the Hale telescope: part 2, photon noise theory

High-resolution broadband spectroscopy at near-infrared (NIR) wavelengths (950 to 2450 nm) has been performed using externally dispersed interferometry (EDI) at the Hale telescope at Mt. Palomar, with the TEDI interferometer mounted within the central hole of the 200-in. primary mirror in series with the comounted TripleSpec NIR echelle spectrograph. These are the first multidelay EDI demonstrations on starlight. We demonstrated very high (10×) resolution boost and dramatic (20× or more) robustness to point spread function wavelength drifts in the native spectrograph. Data analysis, results, and instrument noise are described in a companion paper (part 1). This part 2 describes theoretical photon limited and readout noise limited behaviors, using simulated spectra and instrument model with noise added at the detector. We show that a single interferometer delay can be used to reduce the high frequency noise at the original resolution (1× boost case), and that except for delays much smaller than the native response peak half width, the fringing and nonfringing noises act uncorrelated and add in quadrature. This is due to the frequency shifting of the noise due to the heterodyning effect. We find a sum rule for the noise variance for multiple delays. The multiple delay EDI using a Gaussian distribution of exposure times has noise-to-signal ratio for photon-limited noise similar to a classical spectrograph with reduced slitwidth and reduced flux, proportional to the square root of resolution boost achieved, but without the focal spot limitation and pixel spacing Nyquist limitations. At low boost (∼1×) EDI has ∼1.4× smaller noise than conventional, and at >10× boost, EDI has ∼1.4× larger noise than conventional. Readout noise is minimized by the use of three or four steps instead of 10 of TEDI. Net noise grows as step phases change from symmetrical arrangement with wavenumber across the band. For three (or four) steps, we calculate a multiplicative bandwidth of 1.8:1 (2.3:1), sufficient to handle the visible band (400 to 700 nm, 1.8:1) and most of TripleSpec (2.6:1)