Search results for "Exponent"
showing 10 items of 896 documents
Connections and geodesics in the space of metrics
2015
We argue that the exponential relation $g_{\mu\nu} = \bar{g}_{\mu\rho}\big(\mathrm{e}^h\big)^\rho{}_\nu$ is the most natural metric parametrization since it describes geodesics that follow from the basic structure of the space of metrics. The corresponding connection is derived, and its relation to the Levi-Civita connection and the Vilkovisky-DeWitt connection is discussed. We address the impact of this geometric formalism on quantum gravity applications. In particular, the exponential parametrization is appropriate for constructing covariant quantities like a reparametrization invariant effective action in a straightforward way. Furthermore, we reveal an important difference between Eucli…
Proper Time Flow Equation for Gravity
2004
We analyze a proper time renormalization group equation for Quantum Einstein Gravity in the Einstein-Hilbert truncation and compare its predictions to those of the conceptually different exact renormalization group equation of the effective average action. We employ a smooth infrared regulator of a special type which is known to give rise to extremely precise critical exponents in scalar theories. We find perfect consistency between the proper time and the average action renormalization group equations. In particular the proper time equation, too, predicts the existence of a non-Gaussian fixed point as it is necessary for the conjectured nonperturbative renormalizability of Quantum Einstein…
Critical behavior of a supersymmetric extension of the Ginzburg-Landau model
2011
We make a connection between quantum phase transitions in condensed matter systems, and supersymmetric gauge theories that are of interest in the particle physics literature. In particular, we point out interesting effects of the supersymmetric quantum electrodynamics upon the critical behavior of the Ginzburg-Landau model. It is shown that supersymmetry fixes the critical exponents, as well as the Landau-Ginzburg parameter, and that the model resides in the type II regime of superconductivity.
Added Value and Clinical Significance of Nonlinear Variability Indices of Walking Stride Interval in Neurodegenerative Diseases
2020
AbstractThough self-paced walking is highly stereotyped, the stride interval fluctuates from one stride to the next around an average value with a measurable statistical variability. In clinical gait analysis, this variability is usually assessed with indices such the standard deviation or the coefficient of variation (CV). The aim of this study is to understand the added value that nonlinear indices of walking stride interval variability, such as Hurst exponent (H) and Minkowski fractal dimension (D), can provide in a clinical context and to suggest a clinical significance of these indices in the most common neurodegenerative diseases: Parkinson, Huntington, and amyotrophic lateral scleros…
Nonlinear Dynamics Techniques for the Detection of the Brain Areas Using MER Signals
2008
A methodology for identifying brain areas from the brain MER signals (microelectrode recordings) is presented, which is based on a nonlinear feature set. We propose nonlinear dynamics measures such as correlation dimension, Hurst exponent and the largest Lyapunov exponent to characterize the dynamic structure. The MER records belong to the Polytechnical University of Valencia, 24 records for each zone (black substance, thalamus, subthalamus nucleus and uncertain area). The detection of each area using characteristics derived from complexity analysis was obtained through a classifier (support vector machine). The joint information between areas is remarkable and the best accuracy result was …
FRACTALITY EVIDENCE AND LONG-RANGE DEPENDENCE ON CAPITAL MARKETS: A HURST EXPONENT EVALUATION
2014
Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is…
Multi-agent-based Order Book Model of financial markets
2006
We introduce a simple model for simulating financial markets, based on an order book, in which several agents trade one asset at a virtual exchange continuously. For a stationary market the structure of the model, the order flow rates of the different kinds of order types and the used price time priority matching algorithm produce only a diffusive price behavior. We show that a market trend, i.e. an asymmetric order flow of any type, leads to a non-trivial Hurst exponent for the price development, but not to "fat-tailed" return distributions. When one additionally couples the order entry depth to the prevailing trend, also the stylized empirical fact of "fat tails" can be reproduced by our …
Statistical analysis of financial returns for a multiagent order book model of asset trading
2007
We recently introduced a realistic order book model [T. Preis, Europhys. Lett. 75, 510 (2006)] which is able to generate the stylized facts of financial markets. We analyze this model in detail, explain the consequences of the use of different groups of traders, and focus on the foundation of a nontrivial Hurst exponent based on the introduction of a market trend. Our order book model supports the theoretical argument that a nontrivial Hurst exponent implies not necessarily long-term correlations. A coupling of the order placement depth to the market trend can produce fat tails, which can be described by a truncated Lévy distribution.
Medium-range interactions and crossover to classical critical behavior
1996
We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be …
A simplified falling-head tecnique for rapid determination of field-saturated hydraulic conductivity
2004
Simplified measurements of the field-saturated hydraulic conductivity, K fs , require short duration experiments, small water volumes, and easily transportable equipment. A simplified falling-head (SFH) technique for the rapid determination of K fs has been developed and tested. The technique consists in applying a small volume of water on a soil surface, confined by a ring inserted a short distance into the soil, and then measuring the time from the application of water to the instant at which the surface area is no longer covered by water. A measurement of the initial and field-saturated soil water contents, and an estimate of the α* parameter of the Gardner's exponential model are then u…