Pell conics and quadratic reciprocity

We give a proof of quadratic reciprocity, based on the arithmetic of conics. The proof works in all cases, and the calculations are remarkably simple

Validation of the frequency modulation technique applied to the pulsating Sct- Dor eclipsing binary star KIC 8569819

KIC 8569819 is an eclipsing binary star with an early F primary and G secondary in a 20.85-d eccentric orbit. The primary is a δ Sct–γ Dor star pulsating in both p modes and g modes. Using four years of Kepler Mission photometric data, we independently model the light curve using the traditional technique with the modelling code PHOEBE, and we study the orbital characteristics using the new frequency modulation technique. We show that both methods provide the equivalent orbital period, eccentricity and argument of periastron, thus illustrating and validating the FM technique. In the amplitude spectrum of the p-mode pulsations, we also discovered an FM signal compatible with a third body in the system, a low-mass M dwarf in an 861-d orbit around the primary pair. However, the eclipses show no timing variations, indicating that the FM signal is a consequence of the intrinsic change in pulsation frequency, thus providing a cautionary tale. Our analysis shows the potential of the FM technique using Kepler data, and we discuss the prospects to detect planets and brown dwarfs in Kepler data for A and F stars even in the absence of transits and with no spectroscopic radial velocity curves. This opens the possibility of finding planets orbiting hotter stars that cannot be found by traditional techniques

Heartbeat stars and the ringing of tidal pulsations

With the advent of high precision photometry from satellites such as Kepler and CoRoT, a whole new layer of interesting and astounding astronomical objects has been revealed: heartbeat stars are an example of such objects. Heartbeat stars are eccen- tric ellipsoidal variables that undergo strong tidal interactions when the stars are almost in contact at the time of closest approach. These interactions deform of the stars and cause a notable light curve variation in the form of a tidal pulse. A subset of these objects (∼20%) show prominent tidally induced pulsations: pulsations forced by the binary orbit. We now have a fully functional code that models binary star features (using phoebe) and stellar pulsations simultaneously, enabling a complete and accurate heartbeat star model to be determined. In this paper we show the results of our new code, which uses emcee, a variant of mcmc, to generate a full set of stellar parameters. We further highlight the interesting features of KIC 8164262, including its tidally induced pulsations and resonantly locked pulsations

Constructions of generalized complex structures in dimension four

Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-manifolds, both simply and non-simply connected, which are neither complex nor symplectic

Effect of Adjusting Pseudo-Guessing Parameter Estimates on Test Scaling When Item Parameter Drift Is Present

In item response theory test scaling/equating with the three-parameter model, the scaling coefficients A and B have no impact on the c-parameter estimates of the test items since the c-parameter estimates are not adjusted in the scaling/equating procedure. The main research question in this study concerned how serious the consequences would be if c-parameter estimates are not adjusted in the test equating procedure when item-parameter drift (IPD) is present. This drift is commonly observed in equating studies and hence, has been the source of considerable research. The results from a series of Monte-Carlo simulation studies conducted under 32 different combinations of conditions showed that some calibration strategies in the study, where the c-parameters were adjusted to be identical across two test forms, resulted in more robust equating performance in the presence of IPD. This paper discusses the practical effectiveness and the theoretical importance of appropriately adjusting c-parameter estimates in equating. Accessed 3,754 times on https://pareonline.net from July 04, 2015 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Physics of Eclipsing Binaries: Heartbeat Stars and Tidally Induced Pulsations

Heartbeat stars are a relatively new class of eccentric ellipsoidal variable first discovered by Kepler. An overview of the current field is given with details of some of the interesting objects identified in our current Kepler sample of 135 heartbeats stars. Three objects that have recently been or are undergoing detailed study are described along with suggestions for further avenues of research. We conclude by discussing why heartbeat stars are an interesting new tool to study tidally induced pulsations and orbital dynamics

Signal transducer and activator of transcription 2 deficiency is a novel disorder of mitochondrial fission

Defects of mitochondrial dynamics are emerging causes of neurological disease. In two children presenting with severe neurological deterioration following viral infection we identified a novel homozygous STAT2 mutation, c.1836C4A (p.Cys612Ter), using whole exome sequencing. In muscle and fibroblasts from these patients, and a third unrelated STAT2-deficient patient, we observed extremely elongated mitochondria. Western blot analysis revealed absence of the STAT2 protein and that the mitochondrial fission protein DRP1 (encoded by DNM1L) is inactive, as shown by its phosphorylation state. All three patients harboured 15 decreased levels of DRP1 phosphorylated at serine residue 616 (P-DRP1S616), a post-translational modification known to activate DRP1, and increased levels of DRP1 phosphorylated at serine 637 (P-DRP1S637), associated with the inactive state of the DRP1 GTPase. Knockdown of STAT2 in SHSY5Y cells recapitulated the fission defect, with elongated mitochondria and decreased PDRP1 S616 levels. Furthermore the mitochondrial fission defect in patient fibroblasts was rescued following lentiviral transduction with wild-type STAT2 in all three patients, with normalization of mitochondrial length and increased P-DRP1S616 levels. Taken 20 together, these findings implicate STAT2 as a novel regulator of DRP1 phosphorylation at serine 616, and thus of mitochondrial fission, and suggest that there are interactions between immunity and mitochondria. This is the first study to link the innate immune system to mitochondrial dynamics and morphology. We hypothesize that variability in JAK-STAT signalling may contribute to the phenotypic heterogeneity of mitochondrial disease, and may explain why some patients with underlying mitochondrial disease decompensate after seemingly trivial viral infections. Modulating JAK-STAT activity may represent a novel 25 therapeutic avenue for mitochondrial diseases, which remain largely untreatable. This may also be relevant for more common neurodegenerative diseases, including Alzheimer’s, Huntington’s and Parkinson’s diseases, in which abnormalities of mitochondrial morphology have been implicated in disease pathogenesis

An Application of Item Response Theory to Psychological Test Development

Item response theory (IRT) has become a popular methodological framework for modeling response data from assessments in education and health; however, its use is not widespread among psychologists. This paper aims to provide a didactic application of IRT and to highlight some of these advantages for psychological test development. IRT was applied to two scales (a positive and a negative affect scale) of a self-report test. Respondents were 853 university students (57 % women) between the ages of 17 and 35 and who answered the scales. IRT analyses revealed that the positive affect scale has items with moderate discrimination and are measuring respondents below the average score more effectively. The negative affect scale also presented items with moderate discrimination and are evaluating respondents across the trait continuum; however, with much less precision. Some features of IRT are used to show how such results can improve the measurement of the scales. The authors illustrate and emphasize how knowledge of the features of IRT may allow test makers to refine and increase the validity and reliability of other psychological measures

Effect of dead space on avalanche speed

The effects of dead space (the minimum distance travelled by a carrier before acquiring enough energy to impact ionize) on the current impulse response and bandwidth of an avalanche multiplication process are obtained from a numerical model that maintains a constant carrier velocity but allows for a random distribution of impact ionization path lengths. The results show that the main mechanism responsible for the increase in response time with dead space is the increase in the number of carrier groups, which qualitatively describes the length of multiplication chains. When the dead space is negligible, the bandwidth follows the behavior predicted by Emmons but decreases as dead space increase