Five Years of Phase Space Dynamics of the Standard & Poor’s 500

Abstract

Inhomogeneous density of states in a discrete model of Standard & Poor’s 500 phase space leads to inequitable predictability of market events. Most frequent events might be efficiently predicted in the long run as expected from Mean reversion theory. Stocks have different mobility in phase space. Highly mobile stocks are associated with less unsystematic risk. Less mobile stocks might be cast into disfavor almost indefinitely. Relations between information components in Standard & Poor’s 500 phase space resemble of those in unfair coin tossing.

Analysis of the overvoltage cooperative control strategy for the small hydropower distribution network

“…The main idea of the PSO algorithm is to initialize a group of random particles (random solutions) and then find the optimal solution through iteration. In each iteration, the particle updates itself by tracking two extremums; the first is the optimal solution found by the particle itself, this solution is called the individual extremum; the other extremum is the optimal currently found for the entire population [23][24][25][26][27]. Solution to this extreme value is the global extremum.…”

Infinite Ergodic Walks in Finite Connected Undirected Graphs

“…The information divergence [29] (25) vanishes if and only if the density of t-step precursors Pr(X −t |X) for the location X over the graph G is identical to π(X −t ), so that visiting the location X −t in the past is statistically independent of visiting the present location X t steps later, and therefore X −t is not a t-step precursor of X [30]. The amount of information (25) attains its maximum value, viz.,…”

“…The problem of effective navigation in graphs and networks can be considered in the framework of canonical ensemble of walks, since the navigator location prediction requires a density of locations that is known. Frequently visited sites are predicted more efficiently than little frequented, especially in the long-run [ 30 ].…”

“…The information divergence [ 29 ] ( 25 ) vanishes if and only if the density of t -step precursors for the location X over the graph G is identical to , so that visiting the location in the past is statistically independent of visiting the present location X t steps later, and therefore is not a t -step precursor of X [ 30 ]. The amount of information ( 25 ) attains its maximum value, viz., whenever the marginal probability is the major left eigenvector of the t -step transition matrix , so that for all t and , i.e., visiting any location in the graph G by -walk with probability 1 is a predictor for visiting any other location X t steps later.…”

Application of artificial intelligence algorithm in mathematical modelling and solving

“…These methods have a common feature: self-learning, self-organising, adaptive, simple, universal, robustness, adapting to parallel processing. There is a wide range of applications in parallel search, Lenovo memory, pattern identification and knowledge automatic acquisition [1].…”