It seems that one cannot find many papers relating entropy to sport competitions. Thus, in this paper, I use (i) the Shannon intrinsic entropy (
) as an indicator of "teams sporting value" (or ..."competition performance") and (ii) the Herfindahl-Hirschman index (HHi) as a "teams competitive balance" indicator, in the case of (professional) cyclist multi-stage races. The 2022 Tour de France and 2023 Tour of Oman are used for numerical illustrations and discussion. The numerical values are obtained from classical and and new ranking indices which measure the teams "final time", on one hand, and "final place", on the other hand, based on the "best three" riders in each stage, but also the corresponding times and places throughout the race, for these finishing riders. The analysis data demonstrate that the constraint, "only the finishing riders count", makes much sense for obtaining a more objective measure of "team value" and team performance", at the end of a multi-stage race. A graphical analysis allows us to distinguish various team levels, each exhibiting a Feller-Pareto distribution, thereby indicating self-organized processes. In so doing, one hopefully better relates objective scientific measures to sport team competitions. Moreover, this analysis proposes some paths to elaborate on forecasting through standard probability concepts.
In this article, the approach of network mapping of words in literary texts is extended to “textual factors”: the network nodes are defined as “concepts”; the links are “community connexions.” ...Thereafter, the text network properties are investigated along modern statistical physics approaches of networks, thereby relating network topology and algebraic properties to literary text contents. As a practical illustration, the first chapter of Genesis in the Bible is mapped into a 10-node network, as in the Kabbalah approach, mentioning God (≡
Elohim
). The characteristics of the network are studied starting from its adjacency matrix and the corresponding Laplacian matrix. Triplets of nodes are particularly examined in order to emphasize the “textual (community) connexions” of each agent “emanation,” through the so-called clustering coefficients and the overlap index, hence measuring the “semantic flow” between the different nodes. It is concluded that this graph is a small world network and weakly dis-assortative, because its average local clustering coefficient is significantly higher than a random graph constructed on the same vertex set.
A Universal Rank-Size Law Ausloos, Marcel; Cerqueti, Roy
PloS one,
11/2016, Volume:
11, Issue:
11
Journal Article
Peer reviewed
Open access
A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics ...arguments starting from the Yule-Simon distribution. A modeling is proposed leading to a universal form. A theoretical suggestion for the "best (or optimal) distribution", is provided through an entropy argument. The ranking of areas through the number of cities in various countries and some sport competition ranking serves for the present illustrations.
We study the fundamental differences that separate: Litecoin; Bitcoin Gold; Bitcoin Cash; Ethereum; and Zcash from Bitcoin, and draw some analysis to how these features are appreciated by the market, ...to ultimately make an inference as to how future successful cryptocurrencies may be invented and behave. We use Google Trend data, as well as price, volume and market capitalization data sourced from
coinmarketcap.com
to support this analysis. We find that Litecoin’s shorter block times offer benefits in commerce, but drawbacks in the mining process through orphaned blocks. Zcash holds a niche use for anonymous transactions, benefitting areas of the world lacking in economic freedom. Bitcoin Cash suffers from centralization in the mining process, while the greater decentralization of Bitcoin Gold has generally left it to stagnate. Ether’s greater functionality offers the greatest threat to Bitcoin’s dominance in the market. A coin that incorporates several of these features can be technically better than Bitcoin, but the first-to-market advantage of Bitcoin should keep its dominant position in the market.
Many still rightly wonder whether accounting numbers affect business value. Basic questions are “why?” and “how?” We aim at promoting an objective choice on how optimizing the most suitable valuation ...methods under a “value-based management” framework through some performance measurement systems. First, we present a comprehensive review of valuation methods. Three valuations methods, (i) Free Cash Flow Valuation Model (FCFVM), (ii) Residual Earning Valuation Model (REVM) and (iii) Abnormal Earning Growth Model (AEGM), are presented. We point out advantages and limitations. As applications, the proofs of our findings are illustrated on three study cases: Marks & Spencer’s (M&S’s) business pattern (size and growth prospect), which had a recently advertised valuation “problem”, and two comparable companies, Tesco and Sainsbury’s, all three chosen for multiple-based valuation. For the purpose, two value drivers are chosen, EnV/EBIT (entity value/earnings before interests and taxes) and the corresponding EnV/Sales. Thus, the question whether accounting numbers through models based on mathematical economics truly affect business value has an answer: “Maybe, yes”.
In the framework of applying econophysics ideas in religious topics, the finances of the Antoinist religious movement organised in Belgium between 1920 and 2000 are studied. The interest of ...investigating financial aspects of such a, sometimes called, sect stems in finding characteristics of conditions and mechanisms under which definitely growth and decay features of communities can be understood. The legally reported yearly income and expenses between 1920 and 2000 are studied. A three wave asymmetric regime is observed over a trend among marked fluctuations at times of crises. The data analysis leads to the proposition of a general mechanistic model taking into account an average GDP growth, oscillatory monetary inflation and a logistic population drift.
► The finances of the Antoinist cult in Belgium between 1920 and 2000 are studied. ► Three similar wave asymmetric regimes are observed in specific time intervals. ► Socio–econo conditions for growth & decay features of the community are explained. ► A mathematical model is proposed taking into account ingredients. ► Country GDP growth, oscillatory monetary inflation, logistic population drift.
This paper reports a new methodology and results on the forecast of the numerical value of the fat tail(s) in asset returns distributions using the irrational fractional Brownian motion model. ...Optimal model parameter values are obtained from fits to consecutive daily 2-year period returns of S&P500 index over 1950–2016, generating 33-time series estimations. Through an econometric model, the kurtosis of returns distributions is modelled as a function of these parameters. Subsequently an auto-regressive analysis on these parameters advances the modelling and forecasting of kurtosis and returns distributions, providing the accurate shape of returns distributions and measurement of Value at Risk.
To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The ...proposed cross-sectional intrinsic entropy (
) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices-open, high, low, and close prices (OHLC)-along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the
and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman-Klass, Rogers-Satchell, Yang-Zhang, and intrinsic entropy (
), defined and computed from historical OHLC daily prices of the Standard & Poor's 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the
market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows.
We recall the historically admitted prerequisites of Economic Freedom (EF). We have examined 908 data points for the Economic Freedom of the World (EFW) index and 1884 points for the Index of ...Economic Freedom (IEF); the studied periods are 2000-2006 and 1997-2007, respectively, thereby following the Berlin wall collapse, and including 11 September 2001. After discussing EFW index and IEF, in order to compare the indices, one needs to study their overlap in time and space. That leaves 138 countries to be examined over a period extending from 2000 to 2006, thus 2 sets of 862 data points. The data analysis pertains to the rank-size law technique. It is examined whether the distributions obey an exponential or a power law. A correlation with the country's Gross Domestic Product (GDP), an admittedly major determinant of EF, follows, distinguishing regional aspects, i.e., defining 6 continents. Semi-log plots show that the EFW-rank relationship is exponential for countries of high rank (≥20); overall the log-log plots point to a behaviour close to a power law. In contrast, for the IEF, the overall ranking has an exponential behaviour; but the log-log plots point to the existence of a transitional point between two different power laws, i.e., near rank 10. Moreover, log-log plots of the EFW index relationship to country GDP are characterised by a power law, with a rather stable exponent (γ≃0.674) as a function of time. In contrast, log-log plots of the IEF relationship with the country's gross domestic product point to a downward evolutive power law as a function of time. Markedly the two studied indices provide different aspects of EF.
This paper grounds the critique of the reduction of regions in a country , not only in its geographical and social context but also in its entropic space. The various recent plans leading to the ...reduction of the number of regions in metropolitan France are discussed, based on the mere distribution in the number of municipalities in the plans and analyzed according to various distribution laws. Each case, except the present distribution with 22 regions, on the mainland, does not seem to fit presently used theoretical models. In addition, the number of inhabitants is examined in each plan. The same conclusion holds. Therefore, a theoretical argument based on entropy considerations is proposed, thereby pointing to whether more order or less disorder is the key question—discounting political considerations.
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