Intransitivity in Theory and in the Real World

This work considers reasons for and implications of discarding the assumption of transitivity, which (transitivity) is the fundamental postulate in the utility theory of Von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology, game theory, economics and competitive evolutionary dynamic. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e. approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. Quantum preferences are also considered in the Appendix.Comment: 44 pages, 14 figures, 47 references, 6 appendice

Colorful linear programming, Nash equilibrium , and pivots

The colorful Carathéodory theorem, proved by Barany in 1982, states that given d+1 sets of points S_1,...,S_{d+1} in R^d, such that each S_i contains 0 in its convex hull, there exists a set subset T in the union of the S_i containing 0 in its convex hull and such that T intersects each S_i at most once. An intriguing question - still open - is whether such a set T, whose existence is ensured, can be found in polynomial time. In 1997, Barany and Onn defined colorful linear programming as algorithmic questions related to the colorful Carathéodory theorem. The question we just mentioned comes under colorful linear programming, and there are also other problems. We present new complexity results for colorful linear programming problems and propose a variant of the "Barany-Onn" algorithm, which is an algorithm computing a set T whose existence is ensured by the colorful Carathéodory theorem. Our algorithm makes a clear connection with the simplex algorithm. Some combinatorial applications of the colorful Carathéodory theorem are also discussed from an algorithmic point of view. Finally, we show that computing a Nash equilibrium in a bimatrix game is polynomially reducible to a colorful linear programming problem. On our track, we found a new way to prove that a complementarity problem belongs to the PPAD class with the help of Sperner's lemma

Mutual correlation in the shock wave geometry

We probe the shock wave geometry with the mutual correlation in a spherically symmetric Reissner Nordstr\"om AdS black hole on the basis of the gauge/gravity duality. In the static background, we find that the regions living on the boundary of the AdS black holes are correlated provided the considered regions on the boundary are large enough. We also investigate the effect of the charge on the mutual correlation and find that the bigger the value of the charge is, the smaller the value of the mutual correlation will to be. As a small perturbation is added at the AdS boundary, the horizon shifts and a dynamical shock wave geometry forms after long time enough. In this dynamic background, we find that the greater the shift of the horizon is, the smaller the mutual correlation will to be. Especially for the case that the shift is large enough, the mutual correlation vanishes, which implies that the considered regions on the boundary are uncorrelated. The effect of the charge on the mutual correlation in this dynamic background is found to be the same as that in the static background.Comment: 10 page

Quantifying the loss of processed natural gas within California's South Coast Air Basin using long-term measurements of ethane and methane

Abstract. Methane emissions inventories for Southern California's South Coast Air Basin (SoCAB) have underestimated emissions from atmospheric measurements. To provide insight into the sources of the discrepancy, we analyze records of atmospheric trace gas total column abundances in the SoCAB starting in the late 1980s to produce annual estimates of the ethane emissions from 1989 to 2015 and methane emissions from 2007 to 2015. The first decade of measurements shows a rapid decline in ethane emissions coincident with decreasing natural gas and crude oil production in the basin. Between 2010 and 2015, however, ethane emissions have grown gradually from about 13 ± 5 to about 23 ± 3 Gg yr−1, despite the steady production of natural gas and oil over that time period. The methane emissions record begins with 1 year of measurements in 2007 and continuous measurements from 2011 to 2016 and shows little trend over time, with an average emission rate of 413 ± 86 Gg yr−1. Since 2012, ethane to methane ratios in the natural gas withdrawn from a storage facility within the SoCAB have been increasing by 0.62 ± 0.05 % yr−1, consistent with the ratios measured in the delivered gas. Our atmospheric measurements also show an increase in these ratios but with a slope of 0.36 ± 0.08 % yr−1, or 58 ± 13 % of the slope calculated from the withdrawn gas. From this, we infer that more than half of the excess methane in the SoCAB between 2012 and 2015 is attributable to losses from the natural gas infrastructure