OUTLIERS AND SOME NON-TRADITIONAL MEASURES OF LOCATION IN ANALYSIS OF WAGES

The paper deals with an analysis of how to use certain measures of location in analysis of wages. One of traditional measures of location – the mean should to offer typical value of variable, representing all its values by the best way. Sometimes the mean is located in the tail of the distribution and gives very biased idea about the location of the distribution. The removing of outliers, if any, or using of different measures of location could be useful in these cases. Outliers are characterized and some robust methods of their detecting are described in the paper. Then the trimmed mean and M-estimators are characterized. Computing of one-step M-estimator and modified one-step M-estimator of location is described. The possibilities of using these tools are illustrated on the analysis of the gross yearly wages of employers of one Slovak firm in the year 2013

Multifractal structure of Bernoulli convolutions

Let $\nu_\lambda^p$ be the distribution of the random series $\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. These measures are the well-known (biased) Bernoulli convolutions. In this paper we study the multifractal spectrum of $\nu_\lambda^p$ for typical $\lambda$. Namely, we investigate the size of the sets $$\Delta_{\lambda,p}(\alpha) = \left\{x\in\R: \lim_{r\searrow 0} \frac{\log \nu_\lambda^p(B(x,r))}{\log r} =\alpha\right\}.$$ Our main results highlight the fact that for almost all, and in some cases all, $\lambda$ in an appropriate range, $\Delta_{\lambda,p}(\alpha)$ is nonempty and, moreover, has positive Hausdorff dimension, for many values of $\alpha$. This happens even in parameter regions for which $\nu_\lambda^p$ is typically absolutely continuous.Comment: 24 pages, 2 figure

Self-other differences in student drinking norms research: the role of impression management, self-deception and measurement methodology

Background: Data-driven student drinking norms interventions are based on reported normative overestimation of the extent and approval of an average student’s drinking. Self-reported differences between personal and perceived normative drinking behaviors and attitudes are taken at face value as evidence of actual levels of overestimation. This study investigates whether commonly used data collection methods and socially desirable responding may inadvertently impede establishing 'objective' drinking norms. Methods: UK students [N=421; 69% female; Mean age 20.22 years (SD = 2.5)] were randomly assigned to one of three versions of a drinking norms questionnaire: The standard multi-target questionnaire assessed respondents' drinking attitudes and behaviors (frequency of consumption, heavy drinking, units on a typical occasion) as well as drinking attitudes and behaviors for an ‘average student’. Two deconstructed versions of this questionnaire assessed identical behaviors and attitudes for participants themselves or an 'average student'. The Balanced Inventory of Desirable Responding was also administered. Results: Students who answered questions about themselves and peers reported more extreme perceived drinking attitudes for the average student compared with those reporting solely on the ‘average student’. Personal and perceived reports of drinking behaviors did not differ between multi- and single-target versions of the questionnaire. Among those who completed the multi-target questionnaire, after controlling for demographics and weekly drinking, socially desirable responding was related positively with the magnitude of difference between students’ own reported behaviors/attitudes and those perceived for the average student. Conclusions: Standard methodological practices and socially desirable responding may be sources of bias in peer norm overestimation research

Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles

Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, we study a model where clustering is enhanced by means of a fugacity term as in the Strauss (or "triangle") model, but where the degree sequence is strictly preserved -- thus maintaining the quenched heterogeneity of nodes found in the original degree sequence. Similar models had been proposed previously in [R. Milo et al., Science 298, 824 (2002)]. We find that our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree k > 2 we find a single first order transition. For all non-regular networks that we studied (including Erdos - Renyi and scale-free networks) we find multiple jumps resembling first order transitions, together with strong hysteresis. The latter transitions are driven by the sudden emergence of "cluster cores": groups of highly interconnected nodes with higher than average degrees. To study these cluster cores visually, we introduce q-clique adjacency plots. We find that these cluster cores constitute distinct communities which emerge spontaneously from the triangle generating process. Finally, we point out that cluster cores produce pitfalls when using the present (and similar) models as null models for strongly clustered networks, due to the very strong hysteresis which effectively leads to broken ergodicity on realistic time scales.Comment: 13 pages, 11 figure

The Arecibo Legacy Fast ALFA Survey: The Galaxy Population Detected by ALFALFA

Making use of HI 21 cm line measurements from the ALFALFA survey (alpha.40) and photometry from the Sloan Digital Sky Survey (SDSS) and GALEX, we investigate the global scaling relations and fundamental planes linking stars and gas for a sample of 9417 common galaxies: the alpha.40-SDSS-GALEX sample. In addition to their HI properties derived from the ALFALFA dataset, stellar masses (M_*) and star formation rates (SFRs) are derived from fitting the UV-optical spectral energy distributions. 96% of the alpha.40-SDSS-GALEX galaxies belong to the blue cloud, with the average gas fraction f_HI = M_HI/M_* ~ 1.5. A transition in SF properties is found whereby below M_* ~ 10^9.5 M_sun, the slope of the star forming sequence changes, the dispersion in the specific star formation rate (SSFR) distribution increases and the star formation efficiency (SFE) mildly increases with M_*. The evolutionary track in the SSFR-M_* diagram, as well as that in the color magnitude diagram are linked to the HI content; below this transition mass, the star formation is regulated strongly by the HI. Comparison of HI- and optically-selected samples over the same restricted volume shows that the HI-selected population is less evolved and has overall higher SFR and SSFR at a given stellar mass, but lower SFE and extinction, suggesting either that a bottleneck exists in the HI to H_2 conversion, or that the process of SF in the very HI-dominated galaxies obeys an unusual, low efficiency star formation law. A trend is found that, for a given stellar mass, high gas fraction galaxies reside preferentially in dark matter halos with high spin parameters. Because it represents a full census of HI-bearing galaxies at z~0, the scaling relations and fundamental planes derived for the ALFALFA population can be used to assess the HI detection rate by future blind HI surveys and intensity mapping experiments at higher redshift.Comment: 21 pages (2 columns), 14 figures. Accepted for publication in ApJ. Version with full-resolution figures is available at http://egg.astro.cornell.edu/alfalfa/pubs/Huang2012b_120702.pd

Stochastic perturbations in open chaotic systems: random versus noisy maps

We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate $\kappa$ and dimensions $D$ of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of $\kappa$ and $D$, and show that the improvement of the precision of the estimations with the number of trajectories $N$ is extremely slow ($\propto 1/\ln N$). We also argue that the finite-size $D$ estimators are typically biased. General theoretical results are combined with analytical calculations and numerical simulations in area-preserving baker maps.Comment: 12 pages, 3 figures, 1 table, manuscript submitted to Physical Review

Cell-cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and, little is known about how multicellular signal processing modulates single cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored if cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow Epidermal Growth Factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.Comment: paper + supporting information, total 35 pages, 15 figure