Supernova Brightening from Chameleon-Photon Mixing

Measurements of standard candles and measurements of standard rulers give an inconsistent picture of the history of the universe. This discrepancy can be explained if photon number is not conserved as computations of the luminosity distance must be modified. I show that photon number is not conserved when photons mix with chameleons in the presence of a magnetic field. The strong magnetic fields in a supernova mean that the probability of a photon converting into a chameleon in the interior of the supernova is high, this results in a large flux of chameleons at the surface of the supernova. Chameleons and photons also mix as a result of the intergalactic magnetic field. These two effects combined cause the image of the supernova to be brightened resulting in a model which fits both observations of standard candles and observations of standard rulers.Comment: 17 pages, 3 figure

Pathogenic Variants in Fucokinase Cause a Congenital Disorder of Glycosylation

FUK encodes fucokinase, the only enzyme capable of converting L-fucose to fucose-1-phosphate, which will ultimately be used for synthesizing GDP-fucose, the donor substrate for all fucosyltransferases. Although it is essential for fucose salvage, this pathway is thought to make only a minor contribution to the total amount of GDP-fucose. A second pathway, the major de novo pathway, involves conversion of GDP-mannose to GDP-fucose. Here we describe two unrelated individuals who have pathogenic variants in FUK and who presented with severe developmental delays, encephalopathy, intractable seizures, and hypotonia. The first individual was compound heterozygous for c.667T>C (p.Ser223Pro) and c.2047C>T (p.Arg683Cys), and the second individual was homozygous for c.2980A>C (p.Lys994Gln). Skin fibroblasts from the first individual confirmed the variants as loss of function and showed significant decreases in total GDP-[3H] fucose and [3H] fucose-1-phosphate. There was also a decrease in the incorporation of [5,6-3H]-fucose into fucosylated glycoproteins. Lys994 has previously been shown to be an important site for ubiquitin conjugation. Here, we show that loss-of-function variants in FUK cause a congenital glycosylation disorder characterized by a defective fucose-salvage pathway

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

Long-lived states of oscillator chain with dynamical traps

A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise. Locally they manifest themselves via distortion of the particle arrangement symmetry. Depending on the system parameters the particle arrangement is characterized by the corresponding distributions taking either a bimodal form, or twoscale one, or unimodal onescale form which, however, deviates substantially from the Gaussian distribution. The individual particle velocities exhibit also a number of anomalies, in particular, their distribution can be extremely wide or take a quasi-cusp form. A large number of different cooperative structures and superstructures made of these formations are found in the visualized time patterns. Their evolution is, in some sense, independent of the individual particle dynamics, enabling us to regard them as dynamical phases.Comment: 8 pages, 5 figurs, TeX style of European Physical Journa

Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations

In this paper, the Euler–Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method

Stochastic B-series and order conditions for exponential integrators

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential integrators. The resulting general order theory covers both It\^{o} and Stratonovich integration

The 16-day planetary waves: multi-MF radar observations from the arctic to equator and comparisons with the HRDI measurements and the GSWM modelling results

International audienceThe mesospheric and lower thermospheric (MLT) winds (60?100 km) obtained by multiple MF radars, located from the arctic to equator at Tromsø (70° N, 19° E), Saskatoon (52° N, 107° W), London (43° N, 81° W), Hawaii (21° N, 157° W) and Christmas Island (2° N, 157° W), respectively, are used to study the planetary-scale 16-day waves. Based on the simultaneous observations (1993/1994), the variabilities of the wave amplitudes, periods and phases are derived. At mid- and high-latitude locations the 16-day waves are usually pervasive in the winter-centred seasons (October through March), with the amplitude gradually decreasing with height. From the subtropical location to the equator, the summer wave activities become strong at some particular altitude where the inter-hemisphere wave ducts possibly allow for the leakage of the wave from the other hemispheric winter. The observational results are in good agreement with the theoretical conclusion that, for slowly westward-traveling waves, such as the 16-day wave, vertical propagation is permitted only in an eastward background flow of moderate speed which is present in the winter hemisphere. The wave period also varies with height and time in a range of about 12?24 days. The wave latitudinal differences and the vertical structures are compared with the Global Scale Wave Model (GSWM) for the winter situation. Although their amplitude variations and profiles have a similar tendency, the discrepancies are considerable. For example, the maximum zonal amplitude occurs around 40° N for radar but 30° N for the model. The phase differences between sites due to the latitudinal effect are basically consistent with the model prediction of equatorward phase-propagation. The global 16-day waves at 95 km from the HRDI wind measurements during 1992 through 1995 are also displayed. Again, the wave is a winter dominant phenomenon with strong amplitude around the 40?60° latitude-band on both hemispheres

The δN formula is the dynamical renormalization group

We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model.Comment: v1: 33 pages, plus appendix and references; 5 figures. v2: typographical typos fixed, minor changes to the main text and abstract, reference added; matches version published in JCA