Statistical Picture Research Articles

Influence of angular momentum and Coulomb interaction of colliding nuclei on their multifragmentation

Theoretical calculations are performed to investigate the angular momentum and Coulomb effects on fragmentation and multifragmentation in peripheral heavy-ion collisions at Fermi energies. Inhomogeneous distributions of hot fragments in the freeze-out volume are taken into account by microcanonical Markov chain calculations within the statistical multifragmentation model. Including an angular momentum and a long-range Coulomb interaction between projectile and target residues leads to new features in the statistical fragmentation picture. In this case, one can obtain specific correlations of the sizes of emitted fragments with their velocities and an emission in the reaction plane. In addition, one may see a significant influence of these effects on isotope production both in the midrapidity and in the kinematic regions of the projectile/target. The relation of this approach to the simulations of such collisions with dynamical models is also discussed.

OBJECTIVE MEASUREMENT AND MODELING OF THE LATENT VARIABLES IN EDUCATION

The paper discusses the problem of objective assessment of the latent variables in education. The search for and approbation of the measurement methods adequate for social spheres – including education – is an urgent and relevant task. The author justifies the selection of the Rasch model as a methodological instrument for objective assessment of the latent variables both in social and humanity spheres, and summarizes the implementation experience regarding the assessment of academic achievements of high school leavers in mathematics. In spite of the advantages of the Rasch model, the author draws our attention to the limits of its practical application. However, the experimental results indicate the model’s capability to estimate the academic achievements and education quality. The model gives a valid statistical picture regarding the level of estimated latent variables, and therefore, provides the basis for future predictions and detailed diagnosis of the present.

On the Statistical Properties and Tail Risk of Violent Conflicts

We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data.We introduce a novel approach to apply extreme value theory to fat-tailed variables that have a remote, but nonetheless finite upper bound, by defining a corresponding unbounded dual distribution (given that potential war casualties are bounded by the world population).We apply methods from extreme value theory on the dual distribution and derive its tail properties. The dual method allows us to calculate the real mean of war casualties, which proves to be considerably larger than the sample mean, meaning severe underestimation of the tail risks of conflicts from naive observation. We analyze the robustness of our results to errors in historical reports, taking into account the unreliability of accounts by historians and absence of critical data.We study inter-arrival times between tail events and find that no particular trend can be asserted.All the statistical pictures obtained are at variance with the prevailing claims about long peace, namely that violence has been declining over time.

Chinese Muslims in Canada: a demographic profile and a preliminary test of ethnic saliency

To date, there has been little to no literature examining Chinese Muslim immigrants to Western nations. Recognizing the dearth of such literature, this research presents what appears to be the first-ever descriptive statistical picture of Chinese Muslims migrating to and residing in Canada. By examining how this immigrant population compares to and fares against non-Muslim Chinese and non-Chinese Muslims in Canada with Canadian census data in 1991 and 2001, the research provides preliminary analysis on the saliency of originating Chinese Muslim ethnicity in immigration outcomes. The current findings suggest that with the intersection of cultural and religious identities, Chinese Muslim may experience a different assimilation process compared to non-Muslim Chinese and non-Chinese Muslims.

The magnitudes of the regions 1 and 2 Birkeland currents observed by AMPERE and their role in solar wind‐magnetosphere‐ionosphere coupling

AbstractIn this paper we present the first large‐scale statistical study of the influence of magnetic reconnection on the magnitude of the regions 1 and 2 Birkeland field‐aligned currents (FACs). While previous studies have employed single spacecraft measurements to construct a statistical picture of the location and density of the Birkeland currents, it has hitherto been difficult to compare in situ measurements of the solar wind with instantaneous global field‐aligned current measurements. To that end, we utilize the Active Magnetosphere Planetary Electrodynamics Response Experiment (AMPERE), which yields field‐aligned current density in both hemispheres at a cadence of 10 min. We quantify the amount of current flowing in the regions 1 (R1) and 2 (R2) FACs, and we compare these with the dayside reconnection rate ΦD deduced from interplanetary parameters from the OMNI data set and with the AL index to examine whether magnetic reconnection is responsible for driving currents in the coupled magnetosphere‐ionosphere system. We find that current magnitudes are strongly correlated with both ΦD and AL index. We also find that R1 currents tend to be higher than R2 currents during periods of magnetic reconnection, suggesting leakage of current across the polar cap or an association with the substorm current wedge.

Evolution and mass extinctions as lognormal stochastic processes

AbstractIn a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely calledEvo-SETI. The relevant mathematical tools are:(1)Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black–Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time.(2)The probability distributions known asb-lognormals, i.e. lognormals starting at a certain positive instantb>0 rather than at the origin. Theseb-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists callCladistics.(3)The (Shannon)entropyof suchb-lognormals is then seen to represent the ‘degree of progress’ reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language ofb-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller ‘chaos’), and have their peaks on the increasing GBM exponential. This exponential is thus the ‘trend of progress’ in human history.(4)All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics).(5)But the most striking new result is that the well-known ‘Molecular Clock of Evolution’, namely the ‘constant rate of Evolution at the molecular level’ as shown by Kimura's Neutral Theory of Molecular Evolution,identifieswith growth rate of the entropy of our Evo-SETI model, because they both grewlinearlyin time since the origin of life.(6)Furthermore, we apply our Evo-SETI model to lognormal stochastic processesother than GBMs.For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on aparabolicmean value capable of covering both the extinction and the subsequent recovery of life forms.(7)Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is acubicfunction of the time.In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based uponb-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are theparticular case of exponential growth.

REPAD: An empirical model of pitch angle distributions for energetic electrons in the Earth's outer radiation belt

AbstractWe have recently conducted a statistical survey on pitch angle distributions of energetic electrons trapped in the Earth's outer radiation belt, and a new empirical model was developed based upon survey results. This model—relativistic electron pitch angle distribution (REPAD)—aims to present statistical pictures of electron equatorial pitch angle distributions, instead of the absolute flux levels, as a function of energy, L shell, magnetic local time, and magnetic activity. To quantify and facilitate this statistical survey, we use Legendre polynomials to fit long‐term in situ directional fluxes observed near the magnetic equator from three missions: CRRES, Polar, and LANL‐97A. As the first of this kind of model, REPAD covers the whole outer belt region, providing not only the mean and median pitch angle distributions in the area but also error estimates of the average distributions. Preliminary verification and validation results demonstrate the reliable performance of this model. Usage of REPAD is mainly to predict the full pitch angle distribution of fluxes along a given magnetic field line, or even on a given drift shell, based upon one single unidirectional or omnidirectional flux measurement anywhere on that field line. This can be particularly useful for data assimilation, which usually has large tolerance on data errors. In addition, relatively small variations in pitch angle distributions measured at L shell between ~ 4 and 5 justify the assumption of fixed pitch angle distributions at GPS equatorial crossings (L ~ 4.2) used in our previous studies.

Nationally Based Data: Challenges for Global Governance (and Global Policy)

AbstractThe current statistical picture of the world is probably the best it has ever been. But it also entails major limitations. In this article we show the limitations by focusing on three key areas: security, economy of development and the environment, and argue that they undermine the performance of global governance, and the possibility of global policy. In particular they do not allow taking the full measure and managing optimally the changes underway at the global level. To overcome this state of affairs, upgrading statistical capabilities is critical. To achieve this objective, the article suggests, among other ideas: adjusting and adapting the conceptualization, collection and implementation of statistical data to a world that is on its way to becoming global; improving the conditions of compilation of statistical data in developing countries; and investing in institution‐building and innovation, in developed and developing countries, and in national and international organizations.

Entropy landscape of solutions in the binary perceptron problem

The statistical picture of the solution space for a binary perceptron is studied. The binary perceptron learns a random classification of input random patterns by a set of binary synaptic weights. The learning of this network is difficult especially when the pattern (constraint) density is close to the capacity, which is supposed to be intimately related to the structure of the solution space. The geometrical organization is elucidated by the entropy landscape from a reference configuration and of solution-pairs separated by a given Hamming distance in the solution space. We evaluate the entropy at the annealed level as well as replica symmetric level and the mean field result is confirmed by the numerical simulations on single instances using the proposed message passing algorithms. From the first landscape (a random configuration as a reference), we see clearly how the solution space shrinks as more constraints are added. From the second landscape of solution-pairs, we deduce the coexistence of clustering and freezing in the solution space.

Redesigning a Large Introductory Course to Incorporate the GAISE Guidelines

In 2005, the Guidelines for Assessment and Instruction in Statistics Education (GAISE) college report described several recommendations for teaching introductory statistics. This paper discusses how a large multi-section introductory course was redesigned in order to implement these recommendations. The experience described discusses the key sections of the GAISE report and sheds light on the challenges that must be overcome in putting them in place. The result is a course which addresses both the “how to” and big picture of statistics.

Moduł wskaźników zrównoważonego rozwoju w Banku Danych Lokalnych

Sustainable development is one of the major challenges of the modern world. Its implementation should be monitored at every level of management, with particular emphasis on monitoring the implementation of this concept at the local level (gminas and powiats) and regional (voivodships). The basic assessing tool are indicators to provide a statistical picture of a given territorial unit. Within the Local Data Bank (BDL) a universal module was created, which is designed to monitor sustainable development at a level lower than the country. The reference point were indices developed by the Eurostat. Module developed in the BDL is not a set of monitoring a specific strategy development at local and regional level but is a basic set of indicators for analysis of sustainable development and allows to evaluate and compare local government units.

The morphology of Saturn's ultraviolet aurora

Spectrographic images in the far ultraviolet, obtained from observations made from 2007 to 2009, are used to quantify and compare the morphology of Saturn's northern and southern aurora in local time. Made by the UVIS imager on the Cassini spacecraft, these observations differ from previous UV observations of Saturn's aurora by offering complete local time coverage of the aurora from small zenith angles. A statistical picture emerges after combining over 105 spectrographic images of the north and south aurora. From its composite, the northern aurora exhibits an intensity peak of ∼40 kR near 05 h local time, while the southern aurora peaks at ∼60 kR near the same local time. Aurora intensities in the post‐noon sectors are essentially constant at ∼10 kR. The half‐power points of latitudinal profiles reveal widths of ∼4° near dawn and ∼8° near dusk in both north and south. The aurora has an approximately circular shape (not oval!), although harmonic fits suggest the northern aurora is more nearly circular than the southern. The center of the northern aurora has an offset of ∼1–2° from the pole, while the southern center is offset by ∼2–3°, with both offsets in the midnight‐to‐dawn quadrant. When mapped to the polar regions, precipitation of field‐aligned energetic electrons (>20 keV) generally lies equatorward of the main auroral intensity at all local times.

Learning to Show and Tell Capitalist Style

Mirrors of the Economy: National Accounts and International Norms in Russia and Beyond. By Yoshiko M. Herrera Ithaca, NY: Cornell University Press, 2010. 252 pp., $49.95 hardcover (ISBN 978-08014-4585-9). The collapse of the Soviet Union also saw the end of the particularly Soviet method of national economic accounting. The USSR did not account for its national economic development through the system of national accounts (SNA), the procedure for generating statistical pictures of national economic wealth and development standard in advanced liberal capitalist economies that we take for granted as the means of measuring economic activity. The USSR used the material product system (MPS) and its satellite states followed suit. MPS covered a different range of economic activity to SNA, divided the economy up into different sectors, and had a different headline statistics: where SNA calculates gross domestic product and its components, MPS was concerned with “net material product,” roughly the volume of what was produced, and the balances between economic sectors. The differences between the two systems of national accounting meant that moving from MPS to SNA after the end of communism was a major change both in how statistics were gathered, the use that they could be put to, and the operation and political importance of Goskomstat, the state statistical agency. Such deep-seated and far-reaching change is …

Structure of Leucine Adsorbed on Polystyrene from Nonlinear Vibrational Spectroscopy Measurements, Molecular Dynamics Simulations, and Electronic Structure Calculations

We have used a combination of sum-frequency generation spectroscopy, molecular dynamics simulations, and electronic structure calculations to arrive at a statistical picture of the orientation and ...

Intermediate- and short-range order in phosphorus-selenium glasses

State-of-the-art neutron and x-ray diffraction measurements have been performed to provide a definitive picture of the intermediate- and short-range structures of ${\mathrm{P}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ glasses spanning two glass regions, $x$ $=$ 0.025--0.54 and 0.64--0.84. Liquid ${\mathrm{P}}_{4}$Se${}_{3}$ and amorphous red P and Se were also measured. Detailed information was obtained about the development with increasing phosphorous concentration of intermediate-range order on the length scale \ensuremath{\sim}6 \AA{}, based on the behavior of the first sharp diffraction peak. Attention is also paid to the feature in the structure factor at 7.5 \AA{}${}^{\ensuremath{-}1}$, identified in earlier numerical simulations, provides further evidence of the existence of molecular units. The real-space transforms yield a reliable statistical picture of the changing short-range order as $x$ increases, using the information about types and concentrations of local structural units provided by previous NMR measurements to interpret the trends observed.

Higher order statistics of weak lensing shear and flexion

Owing to their more extensive sky coverage and tighter control on systematic errors, future deep weak lensing surveys should provide a better statistical picture of the dark matter clustering beyond the level of the power spectrum. In this context, the study of non-Gaussianity induced by gravity can help tighten constraints on the background cosmology by breaking parameter degeneracies, as well as throwing light on the nature of dark matter, dark energy or alternative gravity theories. Analysis of the shear or flexion properties of such maps is more complicated than the simpler case of the convergence due to the spinorial nature of the fields involved. Here we develop analytical tools for the study of higher order statistics such as the bispectrum (or trispectrum) directly using such maps at different source redshift. The statistics we introduce can be constructed from cumulants of the shear or flexions, involving the cross-correlation of squared and cubic maps at different redshifts. Typically, the low signal-to-noise ratio prevents recovery of the bispectrum or trispectrum mode by mode. We define power spectra associated with each multispectrum which compress some of the available information of higher order multispectra. We show how these can be recovered from noisy observational data even in the presence of an arbitrary mask, which introduces mixing between electric (E-type) and magnetic (B-type) polarization, in an unbiased way. We also introduce higher order cross-correlators which can cross-correlate lensing shear with different tracers of large-scale structures.

Diversity and difference in early modern London

Jacob Selwood, Diversity and Difference in Early Modern London, Farnham & Burlington, VT, Ashgate, 2010, pp. xii + 214, hb. £55.00, ISBN: 978-0- 7546-6375-1This imaginative contribution to the history of early modern London considers an underexplored facet of civic identity: the encounter between London's citizenry and those 'strangers' who comprised a prominent part of London life, a recognisably non-English presence in the metropolis predating our usual narratives of globalisation. Selwood's focus is on the understanding of 'difference' as a category which transcended any single national group, and one which was open to interpretation and negotiation, particularly regarding those whose parents were born overseas. His interest is in 'the daily practice' of 'defining and policing difference' (p. 6), rather than simply its representation. It is a story of strangers lobbying to escape their marginal status and gain a foothold in the civic community, often with the tacit support of the crown, whilst citizens sought to maintain the boundaries of their community.Chapter one sets the stage with an overview of the changing place of strangers over the period as a whole, usefully synthesising a range of secondary literature. Although the statistical picture is frustratingly imprecise, a general trend of falling numbers in the first half of the seventeenth century, followed by new influxes of immigrants in the second, gives some degree of clarity. This chapter also surveys the institutions which aliens had to negotiate in order to gain a place in London society, notably the guilds, both a barrier and an access point, although even guild membership did not entirely negate marginal status or lead to citizen status. In practice, the securest way for an outsider to secure a foothold in urban society was through money or patronage, a situation not so unfamiliar today.The following chapters are more original in terms of research. Chapter two surveys the understandings of difference expressed in Londoners' petitions protesting about the threat of competition from aliens. To members of trading guilds such as the Company of Weavers, aliens were a threat to the integrity of their trade on several levels. Such companies were partly intended to tame the forces of competition within particular trades and thus maintain a degree of equity amongst members: the toleration of rival societies of artisans, unencumbered by regulation and apparently closed to Englishmen, presented an inexcusable source of competition. Because such practices were supposedly passed on to second generation immigrants, they remained for many Londoners a foreign presence within the nation, 'a common weal among themselves' (p. 61). But whereas the company elites favoured integrating the aliens into their own bodies, thus absorbing some of their innovatory practices, the 'commonalty' feared the consequences of this. …

Geochemical portray of the Pacific Ridge: New isotopic data and statistical techniques

Samples collected during the PACANTARCTIC 2 cruise fill a sampling gap from 53° to 41° S along the Pacific Antarctic Ridge (PAR). Analysis of Sr, Nd, Pb, Hf, and He isotope compositions of these new samples is shown together with published data from 66°S to 53°S and from the EPR. The recent advance in analytical mass spectrometry techniques generates a spectacular increase in the number of multidimensional isotopic data for oceanic basalts. Working with such multidimensional datasets generates a new approach for the data interpretation, preferably based on statistical analysis techniques.Principal Component Analysis (PCA) is a powerful mathematical tool to study this type of datasets. The purpose of PCA is to reduce the number of dimensions by keeping only those characteristics that contribute most to its variance. Using this technique, it becomes possible to have a statistical picture of the geochemical variations along the entire Pacific Ridge from 70°S to 10°S. The incomplete sampling of the ridge led previously to the identification of a large-scale division of the south Pacific mantle at the latitude of Easter Island. The PCA method applied here to the completed dataset reveals a different geochemical profile. Along the Pacific Ridge, a large-scale bell-shaped variation with an extremum at about 38°S of latitude is interpreted as a progressive change in the geochemical characteristics of the depleted matrix of the mantle. This Pacific Isotopic Bump (PIB) is also noticeable in the He isotopic ratio along-axis variation. The linear correlation observed between He and heavy radiogenic isotopes, together with the result of the PCA calculation, suggests that the large-scale variation is unrelated to the plume–ridge interactions in the area and should rather be attributed to the partial melting of a marble-cake assemblage.

A statistical picture of popularization activities and their evolutions in France

This paper provides a detailed statistical picture of French scientists involved in public outreach. This is achieved by analysing the popularization practices of 7000 scientists in all major disciplines over a six-year period (2004 to 2009). I analyse the influence of discipline, position, age and academic productivity. Thanks to a temporal analysis, I show that scientists can be split into three distinct populations with radically different popularization practices. Finally, this analysis suggests that the recent increase in public engagement is the result of heightened social interest which pulls more outreach from particular disciplines.

Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 1960s. This problem finds applications spanning from the mathematician’s pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ∼55% (named random loose packing, RLP) while filling all the loose voids results in a maximum density of ∼63%–64% (named random close packing, RCP). While those values seem robustly true, to this date there is no well-accepted physical explanation or theoretical prediction for them. Here we develop a common framework for understanding the random packings of monodisperse hard spheres whose limits can be interpreted as the experimentally observed RLP and RCP. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach ‘a la Edwards’ (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volumes of the constituent grains (denoted the volume function) and the number of neighbors in contact that permits us to simply combine the two approaches to develop a theory of volume fluctuations in jammed matter. Ultimately, our results lead to a phase diagram that provides a unifying view of the disordered hard sphere packing problem and further sheds light on a diverse spectrum of data, including the RLP state. Theoretical results are well reproduced by numerical simulations that confirm the essential role played by friction in determining both the RLP and RCP limits. The RLP values depend on friction, explaining why varied experimental results can be obtained.