The cause of universality in growth fluctuations

Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth fluctuations. The fluctuations display characteristic features, including double exponential scaling in the body of the distribution and power law scaling of the standard deviation as a function of size. To explain this we propose a remarkably simple additive replication model: At each step each individual is replaced by a new number of individuals drawn from the same replication distribution. If the replication distribution is sufficiently heavy tailed then the growth fluctuations are Levy distributed. We analyze the data from bird populations, firms, and mutual funds and show that our predictions match the data well, in several respects: Our theory results in a much better collapse of the individual distributions onto a single curve and also correctly predicts the scaling of the standard deviation with size. To illustrate how this can emerge from a collective microscopic dynamics we propose a model based on stochastic influence dynamics over a scale-free contact network and show that it produces results similar to those observed. We also extend the model to deal with correlations between individual elements. Our main conclusion is that the universality of growth fluctuations is driven by the additivity of growth processes and the action of the generalized central limit theorem.Comment: 18 pages, 4 figures, Supporting information provided with the source files

Returning children home from care: What can be learned from local authority data?

International Human Rights and child rights conventions as well as U.K. wide legislation and guidance require that children in care should be returned home to one or both parents wherever possible. Reunification with parents is the most common route out of care, but rates of re‐entry are often higher than for other exit routes. This study used 8 years of administrative data (on 2,208 care entrants), collected by one large English local authority, to examine how many children were returned home and to explore factors associated with stable reunification (not re‐entering care for at least 2 years). One‐third of children (36%) had been reunified, with adolescent entrants being the most likely age group to return home. Three quarters (75%) of reunified children had a stable reunification. In a fully adjusted regression model, age at entry, being on a care order prior to return home, staying longer in care, being of minority ethnicity, and having fewer placements in care were all significant in predicting chances of stable reunification. The results underline the importance of properly resourcing reunification services. The methods demonstrate the value to local authorities of analysing their own data longitudinally to understand the care pathways for children they look after

Anomalous price impact and the critical nature of liquidity in financial markets

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the "square-root" impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.Comment: 16 pages, 7 figure

Long-range memory model of trading activity and volatility

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential equation as a dynamical model of the observed memory in the financial time series. The continuous stochastic process reproduces the statistical properties of the trading activity and serves as a background model for the modeling waiting time, return and volatility. Empirically observed statistical properties: exponents of the power-law probability distributions and power spectral density of the long-range memory financial variables are reproduced with the same values of few model parameters.Comment: 12 pages, 5 figure

Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis

Who Are The Social "Entrepreneurs" and What Do They Actually Do?

There is increasing interest in the social entrepreneur and the process of social entrepreneurship. This has led to criticisms of fuzziness surrounding these concepts. This paper explores the concept of the social entrepreneur, considering whether social entrepreneurs can really be termed "entrepreneurs" or if they are something else - individuals motivated by meeting social objectives to achieve social change. Drawing on structuration theory, we place the agent (a social entrepreneur) in the structure (a social system/the context), arguing that they are engaged in a process of co-constructing the current momentum in social entrepreneurship development

Effects of Neutron Irradiation on Carbon Doped MgB2 Wire Segments

We have studied the evolution of superconducting and normal state properties of neutron irradiated Mg(B$_{.962}$C$_{.038}$)$_2$ wire segments as a function of post exposure annealing time and temperature. The initial fluence fully suppressed superconductivity and resulted in an anisotropic expansion of the unit cell. Superconductivity was restored by post-exposure annealing. The upper critical field, H$_{c2}$(T=0), approximately scales with T$_c$ starting with an undamaged T$_c$ near 37 K and H$_{c2}$(T=0) near 32 T. Up to an annealing temperature of 400 $^ o$C the recovery of T$_c$ tends to coincide with a decrease in the normal state resistivity and a systematic recovery of the lattice parameters. Above 400 $^ o$C a decrease in order along the c- direction coincides with an increase in resistivity, but no apparent change in the evolution of T$_c$ and H$_{c2}$. To first order, it appears that carbon doping and neutron damaging effect the superconducting properties of MgB$_2$ independently

Infrared aircraft measurements of stratospheric composition over Antarctica during September 1987

The JPL Mark IV interferometer recorded high resolution, infared solar spectra from the NASA DC-8 aircraft during flights over Antarctica in September 1987. The atmospheric absorption features in these spectra were analyzed to determine the overburdens of O3, NO, NO2, HNO3, ClONO2, HCl, HF, CH4, N2O, CO, H2O and CFC-12. The spectra were obtained at latitudes which ranged between 64 degrees S and 86 degrees S, allowing the composition in the interior of the polar vortex to be compared with that at the edge. The latitude dependence observed for NO, HO2, HNO3, ClONO2, HCl and HF are summerized. The values at 30 deg S were observed on the ferry flight from New Zealand to Hawaii. The dashed lines connecting the two were interpolated across the region for which there are no measurements. The chemically perturbed region is seen to consist of a collar of high HNO3 and ClONO2 surrounding a core in which the overburdens of these and of HCl and NO2 are very low. Clear increases in the overburdens of HF and HNO3 were observed during the course of September in the vortex core. HCl and NO2 exhibited smaller, less significant increases. The overburdens of the tropospheric source gases, N2O, CH4, CF2Cl2, and H2O were observed to much smaller over Antarctica than at mid-latitudes. This, together with the fact that HF over Antarctica was more that double its mid-latitude value, suggests that downwelling has occurred

Psychological, psychophysical, and ergogenic effects of music in swimming

OBJECTIVES: Existing work using dry land exercise-related activities has shown that the careful application of music can lead to a range of benefits that include enhanced affect, lower perceived exertion, greater energy efficiency, and faster time trial performances. The purpose of this study was to assess the psychological, psychophysical, and ergogenic effects of asynchronous music in swimming using a mixed-methods approach. DESIGN: A mixed-model design was employed wherein there was a within-subjects factor (two experimental conditions and a control) and a between-subjects factor (gender). The experimental component of the study was supplemented by qualitative data that were analysed using inductive content analysis. METHODS: Twenty six participants (Mage = 20.0 years, age range: 18–23 years) underwent a period of habituation with Speedo Aquabeat MP3 players prior to the experimental phase. They were then administered two experimental trials (motivational and oudeterous music at 130 bpm) and a no-music control, during which they engaged in a 200-m freestyle swimming time trial. RESULTS: Participants swam significantly faster when exposed to either music condition relative to control (p = .022, ηp2=.18). Moreover, the music conditions were associated with higher state motivation (p = .016, ηp2=.15) and more dissociative thoughts (p = .014, ηp2=.16). CONCLUSIONS: Findings supported the hypothesis that the use of asynchronous music during a high-intensity task can have an ergogenic effect; this was in the order of 2% when averaged out across the two experimental conditions. The use of music, regardless of its motivational qualities, resulted in higher self-reported motivation as well as more dissociative thoughts

Random polynomials, random matrices, and LL-functions

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit