Validation of a Single Inertial Sensor for Measuring Running Kinematics Overground During a Prolonged Run

This article is made available in accordance with the publisher's statement on Open access.Introduction: The purpose of this study was to validate acceleration data from a single inertial sensor containinga tri-axial accelerometer, whilst running overground during a prolonged run against a motion analysis system. Methods: An inertial sensor was placed on the low back of 10 runners who performed an 8 km run on a treadmill.To provide validation of the sensor, data were collected as runners ran along a runway through a motion analysis system at the beginning and throughout the run.Results: High levels of agreement between the two systems were found in the craniocaudal and mediolateral acceleration, with antero posterior having the least agreement with greatest Typical Error of the Estimate (0.66 sample points). Very high to extremely high correlations across all testing times were found in all three directions of accelerations (r=0.75 to 0.95). Heel strike and toe off events were identified in anteroposterior and craniocaudal acceleration, with high levels of agreement and extremely high correlations (r=0.99) between the two systems.Minimal variation and change in agreement and correlation between the data at each testing time were found. Discussion: This study provides evidence that a single inertial sensor placed on the low back is valid for measuring three-dimensional acceleration in overground running during a prolonged run. Further analysis identified specific events of heel strike and toe off and were comparable between the two systems. The minimal variation and change in agreement between the two systems during the run indicates the adherence method of the inertial sensor was suitable. Conclusions: The results of this study indicate that data collected from a single inertial sensor is highly correlated with simultaneous data collected using a motion analysis system, and has the capability to identify heelstrike and toe off events in overground running throughout a prolonged fatiguing run

Ground State Energy of the One-Dimensional Discrete Random Schr\"{o}dinger Operator with Bernoulli Potential

In this paper, we show the that the ground state energy of the one dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is controlled asymptotically as the system size N goes to infinity by the random variable \ell_N, the length the longest consecutive sequence of sites on the lattice with potential equal to zero. Specifically, we will show that for almost every realization of the potential the ground state energy behaves asymptotically as $\frac{\pi^2}{\ell_N+1)^2}$ in the sense that the ratio of the quantities goes to one

Extreme values and fat tails of multifractal fluctuations

In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with such data. We show that because of strong correlations, standard extreme value approach is not valid and classical tail exponent estimators should be interpreted cautiously. Extreme statistics associated with multifractal random processes turn out to be characterized by non self-averaging properties. Our considerations rely upon some analogy between random multiplicative cascades and the physics of disordered systems and also on recent mathematical results about the so-called multifractal formalism. Applied to financial time series, our findings allow us to propose an unified framemork that accounts for the observed multiscaling properties of return fluctuations, the volatility clustering phenomenon and the observed ``inverse cubic law'' of the return pdf tails

Statistically enhanced self-attraction of random patterns

In this work we develop a theory of interaction of randomly patterned surfaces as a generic prototype model of protein-protein interactions. The theory predicts that pairs of randomly superimposed identical (homodimeric) random patterns have always twice as large magnitude of the energy fluctuations with respect to their mutual orientation, as compared with pairs of different (heterodimeric) random patterns. The amplitude of the energy fluctuations is proportional to the square of the average pattern density, to the square of the amplitude of the potential and its characteristic length, and scales linearly with the area of surfaces. The greater dispersion of interaction energies in the ensemble of homodimers implies that strongly attractive complexes of random surfaces are much more likely to be homodimers, rather than heterodimers. Our findings suggest a plausible physical reason for the anomalously high fraction of homodimers observed in real protein interaction networks.Comment: Submitted to PR

Extreme value statistics and return intervals in long-range correlated uniform deviates

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to minimum are such that the reference point from which the maximum is measured is itself a random quantity. We analytically calculate the limiting distributions for independent and identically distributed random variables, and use these as a reference point for correlated cases. The distributions are different from that of the maximum itself i.e., a Weibull distribution, reflecting the fact that the distribution of the reference point either dominates over or convolves with the distribution of the maximum. The functional form of the limiting distributions is unaffected by correlations, although the convergence is slower. We show that our findings can be directly generalized to a wide class of stochastic processes. We also analyze return interval distributions, and compare them to recent conjectures of their functional form

Foundation and empire : a critique of Hardt and Negri

In this article, Thompson complements recent critiques of Hardt and Negri's Empire (see Finn Bowring in Capital and Class, no. 83) using the tools of labour process theory to critique the political economy of Empire, and to note its unfortunate similarities to conventional theories of the knowledge economy

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Last passage percolation and traveling fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\'evy process in this case. The case of bounded jumps yields a completely different behavior

Repositioning of special schools within a specialist, personalised educational marketplace - the need for a representative principle

This paper considers how notions of inclusive education as defined in the United Nations Educational, Scientific and Cultural Organization (UNESCO) Salamanca Agreement (1994) have become dissipated, and can be developed and reframed to encourage their progress. It analyses the discourse within a range of academic, legal and media texts, exploring how this dissipation has taken place within the UK. Using data from 78 specialist school websites it contextualises this change in the use of the terms and ideas of inclusion with the rise of two other constructs, the 'specialist school' and 'personalisation'. It identifies the need for a precisely defined representative principle to theorise the type of school which inclusion aims to achieve, which cannot be subsumed by segregated providers. It suggests that this principle should not focus on the individual, but draw upon a liberal/democratic view of social justice, underlining inclusive education's role in removing social barriers that prevent equity, access and participation for all

Advocacy in the tail: Exploring the implications of ‘climategate’ for science journalism and public debate in the digital age

This paper explores the evolving practices of science journalism and public debate in the digital age. The vehicle for this study is the release of digitally stored email correspondence, data and documents from the Climatic Research Unit at the University of East Anglia in the weeks immediately prior to the United Nations Copenhagen Summit (COP-15) in December 2009. Described using the journalistic shorthand of ‘climategate’, and initially promoted through socio-technical networks of bloggers, this episode became a global news story and the subject of several formal reviews. ‘Climategate’ illustrates that media literate critics of anthropogenic explanations of climate change used digital tools to support their cause, making visible selected, newsworthy aspects of scientific information and the practices of scientists. In conclusion, I argue that ‘climategate’ may have profound implications for the production and distribution of science news, and how climate science is represented and debated in the digitally-mediated public sphere