Key courses of academic curriculum uncovered by data mining of students' grades

Learning is a complex cognitive process that depends not only on an individual capability of knowledge absorption but it can be also influenced by various group interactions and by the structure of an academic curriculum. We have applied methods of statistical analyses and data mining (Principal Component Analysis and Maximal Spanning Tree) for anonymized students' scores at Faculty of Physics, Warsaw University of Technology. A slight negative linear correlation exists between mean and variance of course grades, i.e. courses with higher mean scores tend to possess a lower scores variance. There are courses playing a central role, e.g. their scores are highly correlated to other scores and they are in the centre of corresponding Maximal Spanning Trees. Other courses contribute significantly to students' score variance as well to the first principal component and they are responsible for differentiation of students' scores. Correlations of the first principal component to courses' mean scores and scores variance suggest that this component can be used for assigning ECTS points to a given course. The analyse is independent from declared curricula of considered courses. The proposed methodology is universal and can be applied for analysis of student's scores and academic curriculum at any faculty

The role of emotional variables in the classification and prediction of collective social dynamics

We demonstrate the power of data mining techniques for the analysis of collective social dynamics within British Tweets during the Olympic Games 2012. The classification accuracy of online activities related to the successes of British athletes significantly improved when emotional components of tweets were taken into account, but employing emotional variables for activity prediction decreased the classifiers' quality. The approach could be easily adopted for any prediction or classification study with a set of problem-specific variables.Comment: 16 pages, 9 figures, 2 tables and 1 appendi

Temporal Taylor's scaling of facial electromyography and electrodermal activity in the course of emotional stimulation

High frequency psychophysiological data create a challenge for quantitative modeling based on Big Data tools since they reflect the complexity of processes taking place in human body and its responses to external events. Here we present studies of fluctuations in facial electromyography (fEMG) and electrodermal activity (EDA) massive time series and changes of such signals in the course of emotional stimulation. Zygomaticus major (ZYG, "smiling" muscle) activity, corrugator supercilii (COR, "frowning"bmuscle) activity, and phasic skin conductance (PHSC, sweating) levels of 65 participants were recorded during experiments that involved exposure to emotional stimuli (i.e., IAPS images, reading and writing messages on an artificial online discussion board). Temporal Taylor's fluctuations scaling were found when signals for various participants and during various types of emotional events were compared. Values of scaling exponents were close to 1, suggesting an external origin of system dynamics and/or strong interactions between system's basic elements (e.g., muscle fibres). Our statistical analysis shows that the scaling exponents enable identification of high valence and arousal levels in ZYG and COR signals

Flux calculations in an inhomogeneous Universe: weighting a flux-limited galaxy sample

Many astrophysical problems arising within the context of ultra-high energy cosmic rays, very-high energy gamma rays or neutrinos, require calculation of the flux produced by sources tracing the distribution of galaxies in the Universe. We discuss a simple weighting scheme, an application of the method introduced by Lynden-Bell in 1971, that allows the calculation of the flux sky map directly from a flux-limited galaxy catalog without cutting a volume-limited subsample. Using this scheme, the galaxy distribution can be modeled up to large scales while representing the distribution in the nearby Universe with maximum accuracy. We consider fluctuations in the flux map arising from the finiteness of the galaxy sample. We show how these fluctuations are reduced by the weighting scheme and discuss how the remaining fluctuations limit the applicability of the method.Comment: 8 pages, 10 figures, accepted for publication in MNRA

Long-term IR Photometry of Seyferts

Long-term (up to 10000d) monitoring has been undertaken for 41 Seyferts in the near-IR (JHKL). All but 2 showed variability, with K ampl in the range <0.1 to > 1.1 mags. The timescale for detectable change is from about one week to a few years. A simple cross-correlation study shows evidence for delays of up to several hundred days between the variations seen at the shortest wavelengths and the longest in many galaxies. In particular, the data for F9 now extend to twice the interval covered earlier and the delay between its UV and IR outputs persists. An analysis of the fluxes shows that, for any given galaxy, the colours of the variable component are usually independent of the level of activity. The state of activity can be parameterized. Taken over the whole sample, the colours of the variable components fall within moderately narrowly defined ranges. In particular, the H-K colour is appropriate to a black body of temperature 1600K. The H-K excess for a heavily reddened nucleus can be determined and used to find E_{B-V}, which can be compared to the values found from the visible region broad line fluxes. Using flux-flux diagrams, the flux within the aperture from the underlying galaxy can often be determined without the need for model surface brightness profiles. In many galaxies it is apparent that here must be an additional constant contribution from warm dust.Comment: Better quality available from ftp://ftp.saao.ac.za/pub/isg/seyf.pd

A calibrated measure to compare fluctuations of different entities across timescales

© 2020 The Authors. Published by Springer. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1038/s41598-020-77660-4A common way to learn about a system’s properties is to analyze temporal fluctuations in associated variables. However, conclusions based on fluctuations from a single entity can be misleading when used without proper reference to other comparable entities or when examined only on one timescale. Here we introduce a method that uses predictions from a fluctuation scaling law as a benchmark for the observed standard deviations. Differences from the benchmark (residuals) are aggregated across multiple timescales using Principal Component Analysis to reduce data dimensionality. The first component score is a calibrated measure of fluctuations—the reactivityRA of a given entity. We apply our method to activity records from the media industry using data from the Event Registry news aggregator—over 32M articles on selected topics published by over 8000 news outlets. Our approach distinguishes between different news outlet reporting styles: high reactivity points to activity fluctuations larger than expected, reflecting a bursty reporting style, whereas low reactivity suggests a relatively stable reporting style. Combining our method with the political bias detector Media Bias/Fact Check we quantify the relative reporting styles for different topics of mainly US media sources grouped by political orientation. The results suggest that news outlets with a liberal bias tended to be the least reactive while conservative news outlets were the most reactive.The work was partially supported as RENOIR Project by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska–Curie Grant Agreement No. 691152 and by Ministry of Science and Higher Education (Poland), Grant Nos. 34/H2020/2016, 329025/PnH/2016 and by National Science Centre, Poland Grant No. 2015/19/B/ST6/02612. J.A.H. was partially supported by the Russian Scientific Foundation, Agreement #17-71-30029 with co-financing of Bank Saint Petersburg and by POB Research Centre Cybersecurity and Data Science of Warsaw University of Technology within the Excellence Initiative Program—Research University (IDUB).Published onlin

Constructing a bivariate distribution function with given marginals and correlation: application to the galaxy luminosity function

We show an analytic method to construct a bivariate distribution function (DF) with given marginal distributions and correlation coefficient. We introduce a convenient mathematical tool, called a copula, to connect two DFs with any prescribed dependence structure. If the correlation of two variables is weak (Pearson's correlation coefficient $|\rho| <1/3$), the Farlie-Gumbel-Morgenstern (FGM) copula provides an intuitive and natural way for constructing such a bivariate DF. When the linear correlation is stronger, the FGM copula cannot work anymore. In this case, we propose to use a Gaussian copula, which connects two given marginals and directly related to the linear correlation coefficient between two variables. Using the copulas, we constructed the BLFs and discuss its statistical properties. Especially, we focused on the FUV--FIR BLF, since these two luminosities are related to the star formation (SF) activity. Though both the FUV and FIR are related to the SF activity, the univariate LFs have a very different functional form: former is well described by the Schechter function whilst the latter has a much more extended power-law like luminous end. We constructed the FUV-FIR BLFs by the FGM and Gaussian copulas with different strength of correlation, and examined their statistical properties. Then, we discuss some further possible applications of the BLF: the problem of a multiband flux-limited sample selection, the construction of the SF rate (SFR) function, and the construction of the stellar mass of galaxies ($M_*$)--specific SFR ($SFR/M_*$) relation. The copulas turned out to be a very useful tool to investigate all these issues, especially for including the complicated selection effects.Comment: 14 pages, 5 figures, accepted for publication in MNRAS

Structural properties of discs and bulges of early-type galaxies

We have used the EFAR sample of galaxies to study the light distributions of early-type galaxies. We decompose the 2D light distribution of the galaxies in a flattened spheroidal component with a Sersic radial light profile and an inclined disc component with an exponential light profile. We show that the brightest, bulge dominated elliptical galaxies have a fairly broad distribution in the Sersic profile shape parameter n_B, with a median of about 3.7 and a sigma of ~0.9. Other galaxies have smaller n_B values, meaning that spheroids are in general less concentrated than the n_B=4 de Vaucouleurs-law profile. The results of our light decompositions are robust, even though without kinematic information we cannot prove that the spheroids and discs are really pressure- and rotation-supported stellar systems. If we assume that the detected spheroids and discs are indeed separate components, we can draw the following conclusions: 1) the spheroid and disc scale sizes are correlated; 2) bulge-to-total luminosity ratios, bulge effective radii, and bulge n_B values are all positively correlated; 3) the bivariate space density distribution of elliptical galaxies in the (luminosity, scale size)-plane is well described by a Schechter luminosity function in and a log-normal scale-size distribution at a given luminosity; 4) at the brightest luminosities, the scale size distribution of elliptical galaxies is similar to those of bright spiral galaxies; at fainter luminosities the elliptical scale size distribution peaks at distinctly smaller sizes than the spiral galaxy distribution; and 5) bulge components of early-type galaxies are typically a factor 1.5 to 2.5 smaller than the disks of spiral galaxies, while disc components of early-type galaxies are typically twice as large as the discs of spiral galaxies. [abridged]Comment: 16 pages, 18 figures. Accepted for publication in the MNRA

The Bivariate Brightness Function of Galaxies and a Demonstration of the Impact of Surface Brightness Selection Effects on Luminosity Function Estimations

In this paper we fit an analytic function to the Bivariate Brightness Distribution (BBD) of galaxies. It is a combination of the classical Schechter Function convolved with a Gaussian distribution in surface brightness: thus incorporating the luminosity-surface brightness correlation as seen in many recent datasets. We fit this function to a recent measurement of the BBD based on 45,000 galaxies from the two-degree field Galaxy Redshift Survey (Cross et al. 2001). Using a BBF we explore the impact of the limiting detection isophote on classical measures of the galaxy luminosity distribution. If Gaussian corrected magnitudes are used these change to $\Delta M^*_{b_j} \sim 0.38$ mags, $\Delta \phi^* \sim 11$ and $\Delta \alpha < 0.01$ for $\mu_{lim,b_j}=24.0$ mag arcsec$^{-2}$. Hence while the faint-end slope, $\alpha$, appears fairly robust to surface brightness issues, both the $M^*$ and $\phi^*$ values are highly dependent. The range over which these parameters were seen to vary is fully consistent with the scatter in the published values, reproducing the range of observed luminosity densities ($1.1<j_{b_j}<2.2\times10^8h L_{\odot}$Mpc$^{-3}$ see Cross et al. 2001). We conclude that surface brightness selection effects are primarily responsible for this variation. After due consideration of these effects, we derive a value of $j_{b_j}=2.16\times10^8h L_{\odot}$Mpc$^{-3}$.Comment: 10 pages, 7 figures, Accepted by MNRA