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Sports statistics: Trends and random fluctuations in athletics
Abstract
Improvements in the results of athletic competitions are often
considered to stem from better training and equipment, but elements of
chance are always present in athletics and these also contribute. Here
we distinguish between these two effects by estimating the range into
which athletic records would have fallen in the absence of systematic
progress and then comparing this with actual performance results. We
find that only 4 out of 22 disciplines have shown a systematic
improvement, and that annual best results worldwide show saturation in
some disciplines.
... Extreme value theory [1][2][3][4][5] and analysis of sequences of uncorrelated random variables [6,7] provide the basis for understanding record statistics. Records in problems ranging from finance [8][9][10][11] and sport [12] to random structures [13,14] and complex networks [15][16][17] typically involve sequences of correlated random variables. However, current theoretical understanding of extreme values of correlated random variables is still far from complete [18][19][20]. ...
... on the diagonal x = r. This relation, which properly accounts for the upward slip along the boundary, can be derived from the recurrence equation (11b) by repeating the steps leading to (12). We now introduce a new variable y which is a linear combination of record and position ...
... With this transformation of variables (r, x) → (r, y), the diffusion process takes place in the domain y ≥ r ≥ 0, and importantly, the boundary condition (13) simplifies to ∂P/∂r = 0, along the diagonal y = r. According to equation (12), the density P ≡ P (y, r, t) still obeys the diffusion equation ...
We study records generated by Brownian particles in one dimension.
Specifically, we investigate an ordinary random walk and define the record as
the maximal position of the walk. We compare the record of an individual random
walk with the mean record, obtained as an average over infinitely many
realizations. We term the walk "superior" if the record is always above
average, and conversely, the walk is said to be "inferior" if the record is
always below average. We find that the fraction of superior walks, S, decays
algebraically with time, S ~ t^(-beta), in the limit t --> infty, and that the
persistence exponent is nontrivial, beta=0.382258.... The fraction of inferior
walks, I, also decays as a power law, I ~ t^(-alpha), but the persistence
exponent is smaller, alpha=0.241608.... Both exponents are roots of
transcendental equations involving the parabolic cylinder function. To obtain
these theoretical results, we analyze the joint density of superior walks with
given record and position, while for inferior walks it suffices to study the
density as function of position.
... There is a well documented fact that record-breaking has slowed down in the last decades for many athletic disciplines. "Record-breakers face extinction" -comments the New Scientist [1] a recent analysis by Gembris et al. [2]. They point out that only a few disciplines have shown systematic improvements since 1985, thus most of the track and field records are being broken by chance. ...
... Apparent outliers are the world records for discus and javelin throws, note however that technical specifications have changed meanwhile for the javelin in order to decrease peak ranges (endangering the audience on grandstands). The exponential shapes are consistent with a description based on extreme value statistics [2,7]. ...
... The raw probability distribution for geographic latitude of large throws (Fig. 3a) has a highly peaked, irregular shape centered at about 50 • N. If we accept that record-breaking is essentially a random process without a systematic trend [2,9], success rate at a given location should be proportional to the trial rate. Possible correlation between throw ranges and latitude should appear in a histogram weighted properly with the trial rate distribution. ...
In a recent paper, Mizera and Horváth computed the effects of
environmental factors on shot put and hammer throw ranges [J. Biomech.
35, (2002) 785 796]. They found that the geographic location (latitude
and altitude) influences throwing distances as strongly as
meteorological conditions (wind and air density). Considering the small
differences in record-breaking results, they proposed that normalization
to a reference stadium should be introduced. Here we attempt to detect
possible correlations between geographic location and throwing ranges by
using all-time best result lists. Unfortunately the separation of the
effects of different environmental factors is not possible, simply
because they are not documented. Our tests failed to find the expected
correlation. We conclude that the variance of human factors seems to
dominate, thus any correction of measured results is probably
unnecessary.
... Correlations between data fluctuations would be meaningless if random factors caused fluctuations in sports world records. To explore the presence of randomness in these fluctuations, the impact of random factors on world record fluctuations was evaluated using Gembris predictive statistical model [1,7]. The annual world record fluctuation is presumed to be a smooth stochastic process devoid of systematic progression and adheres to a Gaussian distribution (mean μ and standard deviation σ). ...
... Predictive analyses of sports world records from 1992 to 2018 can be conducted using Gembris algorithmic model [1,7]. The stochastic variation process of 400m and 3000m middle-distance running world records aligns well with the actual performance evolution, indicating a small approximation error and a superior fit of the prediction model for these two sports. ...
Background
Sports records hold valuable insights into human physiological limits. However, presently, there is a lack of integration and evolutionary patterns in the recorded information across various sports.
Methods
We selected sports records from 1992 to 2018, covering 24 events in men’s track, field, and swimming. The Gembris prediction model calculated performance randomness, and Pearson correlation analysis assessed network relevance between projects. Quantitative study of model parameters revealed the impact of various world records’ change range, predicted value, and network correlation on evolutionary patterns.
Results
1) The evolution range indicates that swimming events generally have a larger annual world record variation than track and field events; 2) Gembris’s predictions show that sprint, marathon, and swimming records outperform their predicted values annually; 3) Network relevance analysis reveals highly significant correlations between all swimming events and sprints, as well as significant correlations between marathon and all swimming events.
Conclusion
Sports record evolution is closely linked not only to specific sports technology but also to energy expenditure. Strengthening basic physical training is recommended to enhance sports performance.
... Records are ubiquitous in nature: in sports, climate science, finance, disordered systems, earthquake models, etc [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]-for a recent review see reference [19]. Let us consider a time series in discrete-time with N entries {x 1 , x 2 , . . . ...
... So far, we have seen that the effect of a nonzero staying probability p is to suppress both the mean as well as the variance of the number of records R N up to step N. It is then interesting to know the relative suppression, which is measured by the Fano factor defined in equation (14). Dividing equation (57) by R N (p) we obtain ...
We compute exactly the statistics of the number of records in a discrete-time random walk model on a line where the walker stays at a given position with a nonzero probability 0 ⩽ p ⩽ 1, while with the complementary probability 1 − p, it jumps to a new position with a jump length drawn from a continuous and symmetric distribution f 0(η). We have shown that, for arbitrary p, the statistics of records up to step N is completely universal, i.e. independent of f 0(η) for any N. We also compute the connected two-time correlation function C p (m 1, m 2) of the record-breaking events at times m 1 and m 2 and show it is also universal for all p. Moreover, we demonstrate that C p (m 1, m 2) < C 0(m 1, m 2) for all p > 0, indicating that a nonzero p induces additional anti-correlations between record events. We further show that these anti-correlations lead to a drastic reduction in the fluctuations of the record numbers with increasing p. This is manifest in the Fano factor, i.e. the ratio of the variance and the mean of the record number, which we compute explicitly. We also show that an interesting scaling limit emerges when p → 1, N → ∞ with the product t = (1 − p)N fixed. We compute exactly the associated universal scaling functions for the mean, variance and the Fano factor of the number of records in this scaling limit.
... The statistics of extreme and rare events have recently generated a lot of interest in various areas of science. In particular, the study of the statistics of records in a discrete time series, initiated in the early fifties [1], has become fundamental and important in a wide variety of systems, including climate studies [2,3,4,5,6,7,8,9], finance and economics [10,11,12], hydrology [13], sports [14,15], in detecting heavy tails in statistical distributions [16], and others [17,18]. ...
... where the Kronecker delta, δ(i, j) = 1 if i = j and 0 otherwise, ensures that the size of the sample is N . If one performs the change of variables (14) can be written as ...
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful 'laboratory' to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.
... Our results provide further evidence that the likelihood of upsets is a useful measure of competitiveness in a given sport (Wesson 2002, Lundh 2006. This characterization complements the myriad of available statistics on the outcomes of sports events (Albert 2005, Stern 1991, Gembris 2002. ...
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from season-end standings data and quantify the predictability of games by the frequency of upsets from game results data. We introduce a novel mathematical model in which the underdog team wins with a fixed upset probability. This model quantitatively relates the parity among teams with the predictability of the games, and it can be used to estimate the upset frequency from standings data.
... Much is known in the case, when the entries ξ of the series are so called independent and identically distributed (i.i.d) random variables (RV) drawn from a distribution φ(ξ) [5,6]. Such models have been successfully applied for example in sports [7,8], biological evolution [9], theory of spin glasses [10], or to quantify properties of quantum systems [11,12]. In all of these systems, the entries are completely uncorrelated. ...
We analyse extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that for our data the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.
... It is the study of the statistical properties of particularly large or small values within a data set. EVA is widely applied in various fields where extreme phenomena hold significant importance (Coles 2001;Gilleland and Katz 2016), such as disaster prevention (de Haan and Ferreira 2006;Tippett et al. 2016), finance (Kratz 2019), safety estimation (Songchitruksa and Tarko 2006), sports (Einmahl and Magnus 2008;Gembris et al. 2002), human lifespan (Dong et al. 2016;Rootzen and Zolud 2017), and the recent pandemic (Wong and Collins 2020). Recently, its applications in the biological data analysis has also become active (Basnayake et al. 2019;Tsuduki 2024). ...
Extreme value analysis (EVA) is a statistical method that studies the properties of extreme values of datasets, crucial for fields like engineering, meteorology, finance, insurance, and environmental science. EVA models extreme events using distributions such as Fréchet, Weibull, or Gumbel, aiding in risk prediction and management. This review explores EVA’s application to nanoscale biological systems. Traditionally, biological research focuses on average values from repeated experiments. However, EVA offers insights into molecular mechanisms by examining extreme data points. We introduce EVA’s concepts with simulations and review its use in studying motor protein movements within cells, highlighting the importance of in vivo analysis due to the complex intracellular environment. We suggest EVA as a tool for extracting motor proteins’ physical properties in vivo and discuss its potential in other biological systems. While there have been only a few applications of EVA to biological systems, it holds promise for uncovering hidden properties in extreme data, promoting its broader application in life sciences.
... Next, we aim to extend our conclusions to the finite interaction problem, thus offering us the possibility to strengthen our understanding of MBL physics. Univariate EVT [25][26][27][28][29] has proven useful in fields as diverse as climate science [30][31][32][33] and extreme environmental events [34,35]; structural risks and related safety measures [36,37]; athletic records [38][39][40][41]; finance [42,43]; and statistical physics [29,44]. In particular, disordered condensed matter systems [45] offer a very rich playground for EVT of correlated or uncorrelated random variables, with notable examples such as random matrix theory [46,47], height distribution of surfaces [44,[48][49][50] and spin glasses [51][52][53][54]. ...
Despite a very good understanding of single-particle Anderson localization in one-dimensional (1D) disordered systems, many-body effects are still full of surprises; a famous example is the interaction-driven many-body localization (MBL) problem, about which much has been written, and perhaps the best is yet to come. Interestingly enough the noninteracting limit provides a natural playground to study nontrivial multiparticle physics, offering the possibility to test some general mechanisms with very large-scale exact diagonalization simulations. In this paper, we first revisit the 1D many-body Anderson insulator through the lens of extreme value theory, focusing on the extreme polarizations of the equivalent spin chain model in a random magnetic field. A many-body-induced chain breaking mechanism is explored numerically, and compared to an analytically solvable toy model. A unified description, from weak to large disorder strengths W emerges, where the disorder-dependent average localization length ξ(W) governs the extreme events leading to chain breaks. In particular, tails of the local magnetization distributions are controlled by ξ(W). Remarkably, we also obtain a quantitative understanding of the full distribution of the extreme polarizations, which is given by a Fréchet-type law. In a second part, we explore finite interaction physics and the MBL question. For the available system sizes, we numerically quantify the difference in the extreme value distributions between the interacting problem and the noninteracting Anderson case. Strikingly, we observe a sharp “extreme-statistics transition” as W changes, which may coincide with the MBL transition.
... Next, we aim to extend our conclusions to the finite interaction problem, thus offering us the possibility to strengthen our understanding of MBL physics. Univariate EVT [25][26][27][28][29] has proven useful in fields as diverse as climate science [30][31][32][33] and extreme environmental events [34,35]; structural risks and related safety measures [36,37]; athletic records [38][39][40][41]; finance [42,43]; and statistical physics [29,44]. In particular, disordered condensed matter systems [45] offer a very rich playground for EVT of correlated or uncorrelated random variables, with notable examples such as random matrix theory [46,47], height distribution of surfaces [44,[48][49][50] and spin glasses [51][52][53][54]. ...
Despite a very good understanding of single-particle Anderson localization in one-dimensional (1D) disordered systems, many-body effects are still full of surprises, a famous example being the interaction-driven many-body localization (MBL) problem, about which much has been written, and perhaps the best is yet to come. Interestingly enough the non-interacting limit provides a natural playground to study non-trivial multiparticle physics, offering the possibility to test some general mechanisms with very large-scale exact diagonalization simulations. In this work, we first revisit the 1D many-body Anderson insulator through the lens of extreme value theory, focusing on the extreme polarizations of the equivalent spin chain model in a random magnetic field. A many-body-induced chain breaking mechanism is explored numerically, and compared to an analytically solvable toy model. A unified description, from weak to large disorder strengths W emerges, where the disorder-dependent average localization length governs the extreme events leading to chain breaks. In particular, tails of the local magnetization distributions are controlled by . Remarkably, we also obtain a quantitative understanding of the full distribution of the extreme polarizations, which is given by a Fr\'echet-type law. In a second part, we explore finite interaction physics and the MBL question. For the available system sizes, we numerically quantify the difference in the extreme value distributions between the interacting problem and the non-interacting Anderson case. Strikingly, we observe a sharp "extreme-statistics transition" as W changes, which may coincide with the MBL transition.
... These questions pertain to computing record ages, a quantity that lies at the heart of the subject of record statistics [1][2][3][4][5][6]. The study of record-breaking events has generated immense research interest since the pioneering work of Chandler in 1952 [7], owing to its applications in fields including finance [8][9][10], climate studies [11][12][13][14], hydrology [15], sports [16,17], and also physics [18][19][20][21][22][23]. ...
We propose a universal framework to compute record age statistics of a stochastic time series that undergoes random restarts. The proposed framework makes minimal assumptions on the underlying process and is furthermore suited to treat generic restart protocols going beyond the Markovian setting. After benchmarking the framework for classical random walks on the 1D lattice, we derive a universal criterion underpinning the impact of restart on the age of the n-th record for generic time series with nearest-neighbor transitions. Crucially, the criterion contains a penalty of order n, that puts strong constraints on restart expediting the creation of records, as compared to the simple first-passage completion. The applicability of our approach is further demonstrated on an aggregation-shattering process where we compute the typical growth rates of aggregate sizes. This unified framework paves the way to explore record statistics of time series under restart in a wide range of complex systems.
... For example, the famous book Guinness World Records holds its own record as the bestselling copy righted book in history [1]. Records are also of great interest in sports, especially in athletics and in swimming records, Olympic-or world-records, are always something special and observable [2,3]. ...
... Since σ n = {1, 0} is a binary random variable, its average σ n is just the probability that a record occurs at step n. Below, we show how to compute σ n and from it, the mean number of records R N using equation (16). Suppose that a record occurs at step n, with a record value x > 0 (see figure 3). ...
We compute exactly the mean number of records for a time-series of size N whose entries represent the positions of a discrete time random walker on the line with resetting. At each time step, the walker jumps by a length drawn independently from a symmetric and continuous distribution with probability (with ) and with the complementary probability r it resets to its starting point x=0. This is an exactly solvable example of a weakly correlated time-series that interpolates between a strongly correlated random walk series (for r=0) and an uncorrelated time-series (for ). Remarkably, we found that for every fixed and any N, the mean number of records is completely universal, i.e., independent of the jump distribution . In particular, for large N, we show that grows very slowly with increasing N as for . We also computed the exact universal crossover scaling functions for in the two limits and . Our analytical predictions are in excellent agreement with numerical simulations.
... Extreme values and records have attracted large efforts and attention since the beginnings of statistics and probability, due to their intrinsic interest and their mathematical challenges. An important motivation for studying records comes from their connections with other interesting problems and, of course, from their countless practical applications in different fields such as climatology [1][2][3][4], sports [5][6][7], finance [8,9] or biology [10]. Moreover, records have been used in statistical inference because, in some contexts, data is inherently composed of record observations [11][12][13][14]. ...
The study of records in the linear drift model (LDM) has attracted
much attention recently due to applications in several fields. In the present paper we study δ-records in the LDM, defined as observations which are greater than all previous observations, plus a fixed real quantity δ. We give analytical properties of the probability of δ-records and study the correlation between δ-record events.
We also analyse the asymptotic behaviour of the number of δ-records among the first n observations and give conditions for convergence to the Gaussian distribution. As a consequence of our results, we solve a conjecture posed in J. Stat. Mech. 2010 P10013, regarding the total number of records in an LDM with negative drift.
Examples of application to particular distributions, such as Gumbel or Pareto are also provided. We illustrate our results with a real data
set of summer temperatures in Spain, where the LDM is consistent with the global-warming phenomenon.
... In general, record statistics is expected to be of interest in fields where time series are used and where the size of the entries is a relevant parameter. Such fields include meteorology [1,2], hydrology [3,4], insurance and risk management, trading [5][6][7], economics [8,9], sports [10][11][12][13][14], etc. Another important application concerns current issues of climatology such as global warming where both temperature records [2,[15][16][17][18][19] and rainfall precipitation records [20][21][22] play an important role in anticipating future climatic conditions. ...
We study the statistics of the number of records Rn for a symmetric, n-step, discrete jump process on a 1D lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability distribution. This process includes, as a special case, the standard nearest neighbor lattice random walk. We derive explicitly the generating function of the distribution P(Rn) of the number of records, valid for arbitrary discrete jump distributions. As a byproduct, we provide a relatively simple proof of the generalized Sparre Andersen theorem for the survival probability of a random walk on a line, with discrete or continuous jump distributions. For the discrete jump process, we then derive the asymptotic large n behavior of P(Rn) as well as of the average number of records E(Rn). We show that unlike the case of random walks with symmetric and continuous jump distributions where the record statistics is strongly universal (i.e. independent of the jump distribution for all n), the record statistics for lattice walks depends on the jump distribution for any fixed n. However, in the large n limit, we show that the distribution of the scaled record number Rn/E(Rn) approaches a universal, half-Gaussian form for any discrete jump process. The dependence on the jump distribution enters only through the scale factor E(Rn), which we also compute in the large n limit for arbitrary jump distributions. We present explicit results for a few examples and provide numerical checks of our analytical predictions.
... In recent years the statistics of records have attracted wide interest due to its applications in a large variety of fields, such as meteorology [35][36][37], hydrology [38], finance [39,40] and sports [41,42]: reviews [43,44] discuss in detail record statistics for stochastic processes in one dimension. ...
Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position dependent drift. Though parsimoniously cited both in the physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact result, although lacking translational invariance. We present old and novel results for such model, which moreover we show represents a discrete version of a diffusive particle in the presence of a logarithmic potential.
... What about if the secret behind beating records was to build a new athletic track with a better geometry? Researchers have addressed theoretical issues on various aspects of sport records [1][2][3][4][5] or strategies [6][7][8][9][10], on the effect of running on a bend [11][12][13][14][15], however, little has been done on how to improve the records for running 200 m. Indeed, the more economical way to run is on a straight, but only the 100 m is run straight. ...
We introduce a new optimal control model which encompasses pace optimization and motor control effort for a runner on a fixed distance. The system couples mechanics, energetics, neural drive to an economic decision theory of cost and benefit. We find how effort is minimized to produce the best running strategy, in particular, in the bend. This allows us to discriminate between different types of tracks and estimate the discrepancy between lanes. Relating this model to the optimal path problem called the Dubins path, we are able to determine the geometry of the optimal track and estimate record times.
... And what about if the secret behind beating records was to build a new athletic track with a better geometry? Researchers have addressed theoretical issues on various aspects of sport records [1,2,3,4,5] or strategies [6,7,8,9,10], on the effect of running on a bend [11,12,13,14,15], however little has been done on how to improve the records for running 200m. Indeed, the more economical way to run is on a straight, but only the 100m is run straight. ...
We introduce a new optimal control model which encompasses pace optimization and motor control effort for a runner on a fixed distance. The system couples mechanics, energetics, neural drive to an economic decision theory of cost and benefit. We find how effort is minimized to produce the best running strategy, in particular in the bend. This allows us to discriminate between different types of tracks and estimate the discrepancy between lanes. Relating this model to the optimal path problem called the Dubins path, we are able to determine the geometry of the optimal track and estimate record times.
... The statistics of records have become a subject of great interest in recent years, since it has applications in a large variety of fields, from meteorology [28,29], to economics [30], to sports [31,32]: for reviews in the context of 1-d random processes see [33,34]. In a sequence {x 0 , x 1 , · · · , x n } the event x i is a called a record if it exceeds the values of all the previous data. ...
We consider a persistent random walk on an inhomogeneous environment where the reflection probability depends only on the distance from the origin. Such an environment is the result of an average over all realizations of disorder of a Lévy–Lorentz (LL) gas. Here we show that this averaged Lévy–Lorentz gas yields nontrivial results even when the related LL gas is trivial. In particular, we investigate its long time transport properties such as the mean square displacement and the statistics of records, as well as the occurrence of ageing phenomena.
... Extreme values and records have attracted large efforts and attention since the beginnings of statistics and probability, due to their intrinsic interest and their mathematical challenges. An important motivation for studying records comes from their connections with other interesting problems and, of course, from their countless practical applications in different fields such as climatology [1][2][3][4], sports [5][6][7], finance [8,9] or biology [10]. Moreover, records have been used in statistical inference because, in some contexts, data is inherently composed of record observations [11][12][13][14]. ...
In this paper we prove a Law of Large Numbers for the number of δ -records in a sequence of random variables with an underlying trend. Our results generalizes results appeared in the literature for the i.i.d. case and for records in models with random trend. Two examples to illustrate the application of our results are included.
... [3]). The statistical properties of record-breaking has drawn attention from the stochastic process community [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,21,22,2,23,24,25,26,27,28,29,30]. Generally, this work considers how the underlying properties of a stochastic process relate to properties of the resulting derived process of record-setting events (time between records, for example). ...
World record setting has long attracted public interest and scientific investigation. Extremal records summarize the limits of the space explored by a process, and the historical progression of a record sheds light on the underlying dynamics of the process. Existing analyses of prediction, statistical properties, and ultimate limits of record progressions have focused on particular domains. However, a broad perspective on how record progressions vary across different spheres of activity needs further development. Here we employ cross-cutting metrics to compare records across a variety of domains, including sports, games, biological evolution, and technological development. We find that these domains exhibit characteristic statistical signatures in terms of rates of improvement, "burstiness" of record-breaking time series, and the acceleration of the record breaking process. Specifically, sports and games exhibit the slowest rate of improvement and a wide range of rates of "burstiness." Technology improves at a much faster rate and, unlike other domains, tends to show acceleration in records. Many biological and technological processes are characterized by constant rates of improvement, showing less burstiness than sports and games. It is important to understand how these statistical properties of record progression emerge from the underlying dynamics. Towards this end, we conduct a detailed analysis of a particular record-setting event: elite marathon running. In this domain, we find that studying record-setting data alone can obscure many of the structural properties of the underlying process. The marathon study also illustrates how some of the standard statistical assumptions underlying record progression models may be inappropriate or commonly violated in real-world datasets.
... Recently, the extreme event studies have been developed using various approaches, such as the density of states [3,4], firstpassage and return-time statistics [6][7][8], persistence [9], interoccurrence time statistics [10][11][12] and record statistics [13][14][15]. Among them, there has been considerable interest in investigating the record statistics, which has found many fruitful applications in diverse complex systems, such as spin glasses [16,17], adaptive processes [18], domain wall dynamics [19], avalanche dynamics [20], stock prices [21,22], global warming [23,24], growing network [25], high-temperature superconductors [26], the ant movements dynamics [27], flood dynamics [28], sport statistics [29,30], earthquakes [31,32], and evolutionary biology [33,34]. ...
The record statistics in stationary and non-stationary fractaltime series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions, the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from the results of the stationary case increases by increasing the Hurst exponent in fractional Brownian motions. We demonstrate that the memory governs the dynamics of the records as long as it causes non-stationarity in fractal stochastic processes; otherwise, it has no impact on the record statistics.
... Much is known in the case, when the entries ξ of the series are so called independent and identically distributed (i.i.d) random variables (RV) drawn from a distribution φ(ξ) [5,6]. Such models have been successfully applied for example in sports [7,8], biological evolution [9], theory of spin glasses [10], or to quantify properties of quantum systems [11,12]. In all of these systems, the entries are completely uncorrelated. ...
We analyse extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that for our data the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.
... , x k−1 ). Besides their popularity in our daily life, for instance in the context of sports [9], records have found an increasing number of applications in a variety of complex systems ranging from climate science [10,11] and spin glasses [12] to evolutionary biology [13,14] and finance [15]. In the absence of correlations in the time series, various aspects of record statistics are well understood [16][17][18][19][20][21]. ...
We consider the sequence of records of a strongly correlated time series generated by the positions of a random walker (RW) after n time steps. Denoting by the ordered sequence of the records of the RW, M being the number of records, we focus on the statistics of the record increments , with . We obtain an exact expression for the joint distribution of the record increments 's and the number of records M for a random walk of n steps with arbitrary jump distribution, including L\'evy flights. In particular, we compute explicitly the probability Q(n) that the record increments 's are monotonically decreasing up to step n and show that it is completely universal, i.e., independent of the jump distribution, for any finite n. For large n, we show that , with a universal amplitude .
... For example, the famous book Guinness World Records holds its own record as the bestselling copy righted book in history [1]. Records are also of great interest in sports, especially in athletics and in swimming records, Olympic-or world-records, are always something special and observable [2,3]. ...
... La physique statistique du football est née en 1968 avec les travaux fondateurs de Reep et Benjamin et la théorie des « longues balles » 1 [22,23,24]. Plus tard, le sujet s'est étendu aux statistiques de buts [25,26,27], au nombre de passes effectuées [28] ou aux classements dans les championnats [29] et s'est ouvert à d'autres disciplines [30,31]. ...
Physics tends to understand the world and to find the laws which govern it. Physics of Sports consists in observing with a physicist’s eye the phenomena which happen on the fields. These fields are wide and this study is built on several points which capture our attention : - records sports : to understand the records of speed or strength sports, we focus on muscle contraction mechanisms. We extract the dynamics of a simple gesture at Bench Press and understand it through simple mechanics laws and microscopic model of muscle contraction. - badminton trajectories : we solve the equations of motion of a particle which undergoes gravity and aerodynamic drag (proportional to the velocity sqaure, for high Reynolds numbers) and extract an analytical expression of the range. At each time the launching velocity is higher than the terminal velocity (which is the constant velocity of vertical falling of the projectile under gravity and drag), one observes a Tartaglia triangular shape of the trajectory. It is the case for most of sports balls, for fireworks, for firemen water jets, for cannonballs... For all these trajectories, the range saturates with the initial velocity : even if you hit stronger, the ball will not go further. We show several applications of this property. For exemple in sport, as there is no use to play on a field which is larger than the useful length, the size of sports fields is bound to be linked to the maximal range of the associated ball, from table tennis to golf. - balls impacts : we study soccer kicks and focus on the way of kicking the ball. The toe poke is said to be more efficient than the push pass. We perform experiments which show that the ball velocity does not depend on the shape of the impactor, but only on the velocity of kicking. We then discuss some ways to enhance the impactor velocity by using joints or elasticity of the launcher.
... Questions about how the records increase with time, or the number of records set, are of natural interest in all these complex, sometimes social contexts, have therefore been studied for example, [12,39,31]. A mathematical theory of records for independent identically distributed (i.i.d.) random variables has been developed since the pioneering work of Rényi [32] for example developed in [13,1]. ...
... The notion of records is becoming more and more popular in everyday life as, for instance, one hears and reads more and more often about 'record breaking events'. This is particularly true for sporting events where world or olympic records are often widely covered by the media [1]. In science, record statistics has found many applications in various areas, including in particular natural sciences and finance [2][3][4] where extreme events might have drastic consequences. ...
We study the record statistics of random walks after n steps, x0, x1, ..., xn, with arbitrary symmetric and continuous distribution p(η) of the jumps ηi = xi − xi − 1. We consider the age of the records, i.e. the time up to which a record survives. Depending on how the age of the current last record is defined, we propose three distinct sequences of ages (indexed by α = I, II, III) associated to a given sequence of records. We then focus on the longest lasting record, which is the longest element among this sequence of ages. To characterize the statistics of these longest lasting records, we compute: (i) the probability that the record of the longest age is broken at step n, denoted by Qα(n), which we call the probability of record breaking and: (ii) the duration of the longest lasting record, . We show that both Qα(n) and the full statistics of are universal, i.e. independent of the jump distribution p(η). We compute exactly the large n asymptotic behaviors of Qα(n) as well as (when it exists) and show that each case gives rise to a different universal constant associated to random walks (including Lévy flights). While two of them appeared before in the excursion theory of Brownian motion, for which we provide here a simpler derivation, the third case gives rise to a non-trivial new constant CIII = 0.241 749... associated to the records of random walks. Other observables characterizing the ages of the records, exhibiting an interesting universal behavior, are also discussed.
... What is the most competitive team sport? We answer this question via a statistical survey of an extensive dataset of game results [1][2][3]. We relate parity with predictability and propose the likelihood of upsets as a measure of competitiveness. ...
... Physicists have already recognised sports as a fruitful research field: Statistics of athletic records has been pioneered by Gembris et al. [2] and Wergen et al. [3], for example, and there have been attempts to even predict the limiting performances in the long run [4]. Sports ranking combinatorics has also been considered by Park and Newman [5,6]. ...
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a power law with an exponent close to unity if the competitiveness is a stable quantity and a decisive factor to win a match. Otherwise, the distribution is found narrow. The existing observation of power law distributions in various kinds of real sports tournaments therefore suggests that the rules of those games are constructed in such a way that it is possible to understand the games in terms of the contestants' inherent characteristics of competitiveness.
... What is the most competitive team sport? We answer this question via a statistical survey of an extensive dataset of game results [1][2][3]. We relate parity with predictability and propose the likelihood of upsets as a measure of competitiveness. ...
What is the most interesting team sport? We answer this question via an extensive statistical survey of game scores, consisting of more than 1/4 million games in over a century. We propose the likelihood of upsets as a measure of competitiveness. We demonstrate the utility of this measure via a comparative analysis of several popular team sports including soccer, baseball, hockey, basketball, and football. We also develop a mathematical model, in which the stronger team is favored to win a game. This model allows to us conveniently estimate the likelihood of upsets from the more easily-accessible standings data.
... The statistics of record breaking events in a discrete-time series with independent and identically distributed (i.i.d) entries have been studied in statistics and mathematics literature for a long time [1][2][3]. Recent years have seen a resurgence of interest in record statistics, which play a major role in the analysis of time series in a number of diverse contexts, including sports [4][5][6][7], biological evolution models [8,9], theory of spin-glasses [10,11], models of growing networks [12], analysis of climate data [13][14][15][16][17], and quantum chaos [18]. The quantity of central interest is the mean number of records R n up to step n. ...
We examine distance record setting by a random walker in the presence of a measurement error δ and additive noise γ and show that the mean number of (upper) records up to n steps still grows universally as ⟨R_{n}⟩∼n^{1/2} for large n for all jump densities, including Lévy distributions, and for all δ and γ. In contrast, the pace of record setting, measured by the amplitude of the n^{1/2} growth, depends on δ and γ. In the absence of noise (γ=0), the amplitude S(δ) is evaluated explicitly for arbitrary jump distributions and it decreases monotonically with increasing δ whereas, in the case of perfect measurement (δ=0), the corresponding amplitude T(γ) increases with γ. The exact results for S(δ) offer a new perspective for characterizing instrumental precision by means of record counting. Our analytical results are supported by extensive numerical simulations.
... This is especially true for sports, where world records are always special and noteworthy. 4 More recently, it was realized that records and order statistics play a crucial role in statistical physics. Hence, there has been a surge of interest for these questions in the physics literature. ...
While records and order statistics of independent and identically distributed
(i.i.d.) random variables X_1, ..., X_N are fully understood, much less is
known for strongly correlated random variables, which is often the situation
encountered in statistical physics. Recently, it was shown, in a series of
works, that one-dimensional random walk (RW) is an interesting laboratory where
the influence of strong correlations on records and order statistics can be
studied in detail. We review here recent exact results which have been obtained
for these questions about RW, using techniques borrowed from the study of
first-passage problems. We also present a brief review of the well known (and
not so well known) results for records and order statistics of i.i.d.
variables.
... In recent years researchers from the physics community have started to apply physics-oriented approaches to problems from the area of sports and in particular of soccer [1][2][3]. Specific examples for a quantitative analysis of the outcome of sports events can be found, e.g., in [4][5][6][7][8] and new ranking schemes have been proposed [9]. At first one might think that it is hard to find systematic laws to characterize such complex phenomena as soccer matches. ...
Scoring goals in a soccer match can be interpreted as a stochastic process. In the most simple description of a soccer match one assumes that scoring goals follows from independent rate processes of both teams. This would imply simple Poissonian and Markovian behavior. Deviations from this behavior would imply that the previous course of the match has an impact on the present match behavior. Here a general framework for the identification of deviations from this behavior is presented. For this endeavor it is essential to formulate an a priori estimate of the expected number of goals per team in a specific match. This can be done based on our previous work on the estimation of team strengths. Furthermore, the well-known general increase of the number of the goals in the course of a soccer match has to be removed by appropriate normalization. In general, three different types of deviations from a simple rate process can exist. First, the goal rate may depend on the exact time of the previous goals. Second, it may be influenced by the time passed since the previous goal and, third, it may reflect the present score. We show that the Poissonian scenario is fulfilled quite well for the German Bundesliga. However, a detailed analysis reveals significant deviations for the second and third aspect. Dramatic effects are observed if the away team leads by one or two goals in the final part of the match. This analysis allows one to identify generic features about soccer matches and to learn about the hidden complexities behind scoring goals. Among others the reason for the fact that the number of draws is larger than statistically expected can be identified.
We develop a comprehensive framework for analyzing full-record statistics, covering record counts M(t1),M(t2),..., their corresponding attainment times TM(t1),TM(t2),..., and the intervals until the next record. From this multiple-time distribution, we derive general expressions for various observables related to record dynamics, including the conditional number of records given the number observed at a previous time and the conditional time required to reach the current record given the occurrence time of the previous one. Our formalism is exemplified by a variety of stochastic processes, including biased nearest-neighbor random walks, asymmetric run-and-tumble dynamics, and random walks with stochastic resetting.
The mechanisms underlying the chemo-mechanical coupling of motor proteins is usually described by a set of force-velocity relations that reflect the different mechanisms responsible for the walking behavior of such proteins on microtubules. However, the convexity of such relations remains controversial depending on the species, and in vivo experiments are inaccessible due to the complexity of intracellular environments. As alternative tool to investigate such mechanism, Extreme-value analysis (EVA) can offer insight on the deviations in the data from the median of the probability distributions. Here, we rely on EVA to investigate the motility functions of nanoscale motor proteins in neurons of the living worm Caenorhabditis elegans (C. elegans), namely the motion of kinesin and dynein along microtubules. While the essential difference between the two motors cannot be inferred from the mean velocities, such becomes evident in the EVA plots. Our findings extend the possibility and applicability of EVA for analysing motility data of nanoscale proteins in vivo.
The study of non-stationary behavior in the extremes is important to analyze data in environmental sciences, climate, finance, or sports. As an alternative to the classical extreme value theory, this analysis can be based on the study of record-breaking events. The R package RecordTest provides a useful framework for non-parametric analysis of non-stationary behavior in the extremes, based on the analysis of records. The underlying idea of all the non-parametric tools implemented in the package is to use the distribution of the record occurrence under series of independent and identically distributed continuous random variables, to analyze if the observed records are compatible with that behavior. Two families of tests are implemented. The first only requires the record times of the series, while the second includes more powerful tests that join the information from different types of records: upper and lower records in the forward and backward series. The package also offers functions that cover all the steps in this type of analysis such as data preparation, identification of the records, exploratory analysis, and complementary graphical tools. The applicability of the package is illustrated with the analysis of the effect of global warming on the extremes of the daily maximum temperature series in Zaragoza, Spain.
This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect," where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatiotemporal trends in group composition.
We study the statistics of avalanches, as a response to an applied force, undergone by a particle hopping on a one-dimensional lattice where the pinning forces at each site are independent and identically distributed (i.i.d.), each drawn from a continuous f(x). The avalanches in this model correspond to the interrecord intervals in a modified record process of i.i.d. variables, defined by a single parameter c>0. This parameter characterizes the record formation via the recursive process Rk>Rk−1−c, where Rk denotes the value of the kth record. We show that for c>0, if f(x) decays slower than an exponential for large x, the record process is nonstationary as in the standard c=0 case. In contrast, if f(x) has a faster than exponential tail, the record process becomes stationary and the avalanche size distribution π(n) has a decay faster than 1/n2 for large n. The marginal case where f(x) decays exponentially for large x exhibits a phase transition from a nonstationary phase to a stationary phase as c increases through a critical value ccrit. Focusing on f(x)=e−x (with x≥0), we show that ccrit=1 and for c<1, the record statistics is nonstationary. However, for c>1, the record statistics is stationary with avalanche size distribution π(n)∼n−1−λ(c) for large n. Consequently, for c>1, the mean number of records up to N steps grows algebraically ∼Nλ(c) for large N. Remarkably, the exponent λ(c) depends continuously on c for c>1 and is given by the unique positive root of c=−ln(1−λ)/λ. We also unveil the presence of nontrivial correlations between avalanches in the stationary phase that resemble earthquake sequences.
This work is dealing with the development trends and prognosis in selected men's and women's athletic disciplines until 2016. By the analysis of trends until 2013 were used the time series of the world's best performances until the year 2013 referred to IAAF. The prognosis are given for 4 seasons to the Rio de Janeiro Olympic cycle from 2013-2016 .
By smoothing the data and estimating the prognosed values were used the methods of modeling and trend extrapolation. Due to increase the eccuracy of variability of exact projections was calculated 90 % probability interval for the middle value of the regression function. For each regression line are given values set by prognosis, the value of the upper and lower probability interval, title of the regression line, index of determination R2 and the statistical significance of the slope of the regression function ( p - value ). By the final selection of the regression function, which concretized the trend and prognosed performance, was taken into account the ranking of the world record by the end of 2012, the level of development of the performance in recent years, intra-individual performance of the world's athletes, the index of determination R2 of the approximate function. The selection of the function also reflected the intuitive opinions of experts and specialists from athletic praxis. Estimation and calculation of the prognosed values was implemented in SPSS .
Nowadays we notice a continuous progress of efficiency in some male and female athletic disciplines. By 2013 was noticed the achievement of the prognosed limits - limits of men athletic performance in sprint disciplines (100 m, 200 m, 4x100 m relay ), ski jumping events (long jump, pole vault) and endurance walking sports (20 km and 50 km). Reaching the limits in female performance was noticed in the 4x100 m relay, hammer throw, high jump and endurance walking discipline on 20 km.
In the next four years, from 2013-2016, we can expect improvement in athletic performance and also the improvement of the world records in the men's disciplines 200 m, 800 m, 110 m hurdles and world record in the women's 400 m hurdles run.
The Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position-dependent drift. Though parsimoniously cited both in physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact results, although lacking translational invariance. We present old and novel results for this model, which moreover we show represents a discrete version of a diffusive particle in the presence of a logarithmic potential.
In this paper, the utility and the correlation technique of the detrended cross-correlation analysis and the combined detrended cross-correlation analysis methods are treated for the stochastic properties of the random walk and the Lévy flight via nucleotide sequence data. Data are extracted definitely from twelve genomic DNA sequences (HUMHBB 1-6, Amazonmolly, Bushbaby, Cow, Dolphin, Elephant, and Tarsier) of the GenBank databank. We mainly simulate and analyze scaling exponents for three methods in 1D and 2D random walks and Lévy flights. To compare each other between one gene and the other gene in the twelve genomic DNA sequences, the value of the detrended cross-correlation coefficient ρDCCA in {HUMHBB3} and {Dolphin} genes is shown the largest value 0.214 in the 1D Lévy flight with μ=1.5 compared to other sets. The detrended cross-correlation coefficient ρDCCA in {HUMHBB4} and {HUMHBB6} genes is shown the smallest value -0.231 in the 1D Lévy flight with μ=1.5. We particularly find that the combined detrended cross-correlation coefficient ρCDCCA in the two cases of {HUMHBB3}+{Bushbaby} and {HUMHBB6}+{Dolphin} has the largest value 0.331 in the 1D random walk compared to other sets, while that in {HUMHBB3}+{Tarsier} and {HUMHBB4}+{Elephant} has the smallest value -0.295 in the 1D Lévy flight with μ=1.5.
Extreme value functionals of stochastic processes are inverse functionals of the first passage time—a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for analyzing extreme value statistics of ergodic reversible Markov processes in confining potentials on the hand of the underlying relaxation eigenspectra. We derive a chain of inequalities, which bounds the long-time asymptotics of first passage densities, and thereby extrema, from above and from below. The bounds involve a time integral of the transition probability density describing the relaxation towards equilibrium. We apply our general results to the analysis of extreme value statistics at long times in the case of Ornstein–Uhlenbeck process and a 3D Brownian motion confined to a sphere, also known as Bessel process. We find that even on time-scales that are shorter than the equilibration time, the large deviation limit characterizing long-time asymptotics can approximate the statistics of extreme values remarkably well. Our findings provide a novel perspective on the study of extrema beyond the established limit theorems for sequences of independent random variables and for asymmetric diffusion processes beyond a constant drift.
We study the statistics of increments in record values in a time series {x0=0,x1,x2,…,xn} generated by the positions of a random walk (discrete time, continuous space) of duration n steps. For arbitrary jump length distribution, including Lévy flights, we show that the distribution of the record increment becomes stationary, i.e., independent of n for large n, and compute it explicitly for a wide class of jump distributions. In addition, we compute exactly the probability Q(n) that the record increments decrease monotonically up to step n. Remarkably, Q(n) is universal (i.e., independent of the jump distribution) for each n, decaying as Q(n)∼A/n for large n, with a universal amplitude A=e/π=1.53362….
We investigate the statistics of records in a random sequence
of n time steps. The sequence
's represents the position at step k of a random walk `bridge' of n
steps that starts and ends at the origin. At each step, the increment of the
position is a random jump drawn from a specified symmetric distribution. We
study the statistics of records and record ages for such a bridge sequence, for
different jump distributions. In absence of the bridge condition, i.e., for a
free random walk sequence, the statistics of the number and ages of records
exhibits a `strong' universality for all n, i.e., they are completely
independent of the jump distribution as long as the distribution is continuous.
We show that the presence of the bridge constraint destroys this strong `all
n' universality. Nevertheless a `weaker' universality still remains for large
n, where we show that the record statistics depends on the jump distributions
only through a single parameter , known as the L\'evy index of the
walk, but are insensitive to the other details of the jump distribution. We
derive the most general results (for arbitrary jump distributions) wherever
possible and also present two exactly solvable cases. We present numerical
simulations that verify our analytical results.
Prediction is always a fascinating obsession no matter what we predict. We predict what tomorrow’s weather will be, which team will win the game, who will be the next president of the United States, how fast one will run and how high one will jump, and even how much money we will make next year. Mathematical and statistical models have been used to predict future events in different disciplines. Some prediction models can be used to predict spe-cific magnitudes of an event in the future. For example, because of the high technology development in the last two decades, the models used for weather forecasting became more and more accurate. In some other fields, the predic-tion models are actually not for a specific magnitude of an event in the future but for predicting various developmental trends in the future. For example, statistical models are commonly used for predicting the developmental trends in stocks but not for predicting specific values of the stocks.
The conductors of this study reviewed prediction research and studied the accomplishments and compromises in predicting world records and best performances in track and field and swimming. The results of the study showed that prediction research only promises to describe the historical trends in track and field and swimming performances, to study the limits of human body based on current data, to examine factors that affect human's running, jumping, throwing, and swimming, and to understand the characteristics of human beings. Prediction research cannot accurately predict new world records and future best performances. In the future, prediction research should become an integrated research field consisting of different specialty areas. Researchers need to develop a better model in which random variables could be separated out as independent variables in order to reflect the complex interaction effects and to understand the nature, characteristics, and limitations of humans using world record/best performance data.
We study the statistics of record-breaking events in daily stock prices of
366 stocks from the Standard and Poors 500 stock index. Both the record events
in the daily stock prices themselves and the records in the daily returns are
discussed. In both cases we try to describe the record statistics of the stock
data with simple theoretical models. The daily returns are compared to i.i.d.
RV's and the stock prices are modeled using a biased random walk, for which the
record statistics are known. These models agree partly with the behavior of the
stock data, but we also identify several interesting deviations. Most
importantly, the number of records in the stocks appears to be systematically
decreased in comparison with the random walk model. Considering the
autoregressive AR(1) process, we can predict the record statistics of the daily
stock prices more accurately. We also compare the stock data with simulations
of the record statistics of the more complicated GARCH(1,1) model, which, in
combination with the AR(1) model, gives the best agreement with the
observational data. To better understand our findings, we discuss the survival
and first-passage times of stock prices on certain intervals and analyze the
correlations between the individual record events. After recapitulating some
recent results for the record statistics of ensembles of N stocks, we also
present some new observations for the weekly distributions of record events.
In this dissertation, the dynamics and state formation of different socially-interacting populations of individuals are investigated. People and their encounters are modeled as interacting particle systems and they are studied using statistical physics tools. In the first part, two opinion models in which only alike neighbors interact are presented. The systems evolve via pairwise interaction until either consensus or permanent frustration (diversity) is reached. The simplest of these models corresponds to a population divided in centrists and extremists (rightist and leftists). In 1 dimension a slow relaxation characterized by a non-universal exponent is found. When the population is fully connected an exact expression for the final state probabilities of the species is obtained by mapping the system into a first-passage problem. For the case of many species, a mean-field approximation reveals the transition between consensus and diversity, which is characterized by a divergent time scale and an unusual non-monotonic behavior in the activity of the system. In the second part, a model where people have a continuous and bounded state is studied. Pairs of individuals with different but similar opinions reach an agreement and take their average opinion after interacting, while individuals with widely disparate opinions do not interact. Either a one-party or multi-party final state is found depending on whether the initial range of opinions is smaller or larger respectively than a set threshold. A power law behavior of the density of parties above the threshold is found. The exponent of the transition is estimated using persistence results on the diffusion equation. In the third part, a model that describes the fitness distribution of a competitive population is studied. Agents increase their fitness by winning in a pairwise competition and they decrease it by resting at home. Four different classes of societies are found depending on the ratio between the winning probability and the decline rate. This model is used to compare predictability of games results in 5 major sports leagues. A relation between competitiveness among teams and predictability is found by measuring the percentage of games in which the underdog beat the favorite.
this paper, the authors report, interpret, and extend much of the current understanding of the theory
We address the problem of forecasting the future records for an athletic event on the basis of the observed past records in that event. The records are viewed as realizations of a random process. The bivariate distribution and covariance of the record in any two periods is derived by a simple extension of the theory of order statistics. In the special case of a uniform, normal, or extreme-value parent, minimum-variance-linear-unbiased (MVLU) estimates of the parameters and “best” forecasts of future records may be obtained by generalized least squares. As an illustration, forecasts of the world record in six major running events are calculated for a 15-year period.
New algorithms for correlation analysis are presented that allow the mapping of brain activity from functional MRI (fMRI) data in real time during the ongoing scan. They combine the computation of the correlation coefficients between measured fMRI time-series data and a reference vector with “detrending,” a technique for the suppression of non-stimulus-related signal components, and the “sliding-window technique.” Using this technique, which limits the correlation computation to the last N measurement time points, the sensitivity to changes in brain activity is maintained throughout the whole experiment. For increased sensitivity in activation detection a fast and robust optimization of the reference vector is proposed, which takes into account a realistic model of the hemodynamic response function to adapt the parameterized reference vector to the measured data. Based on the described correlation method, real-time fMRI experiments using visual stimulation paradigms have been performed successfully on a clinical MR scanner, which was linked to an external workstation for image analysis. Magn Reson Med 43:259–268, 2000. © 2000 Wiley-Liss, Inc.
Why are sustained energy budgets of humans and other vertebrates limited to not more than about seven times resting metabolic rate? The answer to this question has potential applications to growth rates, foraging ecology, biogeography, plant metabolism, burn patients and sports medicine.
The effect of Doxorubicin which is (an anthracycline antibiotic with a broad spectrum of antitumor activity) on the monolayer and bilayer in the form of large Multilamellar Vesicles (MLV's) of Dipalmitoyl phosphatidylcholine (DPPC) were studied by means of monolayer techniques (surface pressure, penetration kinetics, and association constant) and light scattering technique. The monolayer technique showed that addition of DXR to a lipid film composed of (DPPC/CHOL/PEG-PE) at a molar ratio of (100:0:0) produced a less condensed Monolayer. In the (pie-A) curves, DXR induced shift towards larger area/molecule, where the area/molecule was shifted from 61 to 89 A2, and 116 A2 in the presence of 20 and 40 nM DXR, respectively. The three curves collapsed at a pressure pi = 45 mN/m. In penetration kinetics experiment (delta pi-t), the change in pressure with time was 8 and 14 mN/m for a DXR concentration of 20 and 40 nM, respectively, and the increase in surface pressure presented a plateau over a period of 30 min. The measured association constant (K) was found to be 5 x 10(5)/M. In the light scattering experiment, there was a shift of the transition temperature (Tm) of (MLV's) of the same composition of the monolayer towards a smaller value from 40.5 degrees to 34.5 degrees C. Incorporation of CHOL and PEG-PE as DPPC/CHOL/PEG-PE at a molar ratio of (100:20:0), (100:20:4) and (100:20:4) greatly counteracted the effect of DXR and made the lipid membrane more condense and rigid. Moreover, the penetration of DXR into the membrane was greatly reduced. There was a very small shift for the (pi-A) and (delta pi-t) curves, and the association constant of the drug for these different lipid compositions was greatly reduced down to 2.5 x 10(5)/M and the transition temperature (Tm) was increased up to (42.5 degrees C) in the presence of 40 nM DXR. Our results suggest that DXR has a great effect on the phospholipid membrane, and that addition of CHOL or PEG-PE to the phospholipid membrane causes stabilization for the membrane, and reduces the interaction with Doxorubicin.
Supplementary information accompanies this communication on Nature’s website. Competing financial interests: declared none
- D Gembris
Gembris, D. et al. Magn. Reson. Med. 43, 259–268 (2000). Supplementary information accompanies this communication on Nature’s website. Competing financial interests: declared none. 506 NATURE | VOL 417| 30 MAY 2002| www.nature.com
The Track and Field Athlete of the Century According to the Statistics (Atk-Pike
- M Koponen