6,895 research outputs found
A new conjecture extends the GM law for percolation thresholds to dynamical situations
The universal law for percolation thresholds proposed by Galam and Mauger
(GM) is found to apply also to dynamical situations. This law depends solely on
two variables, the space dimension d and a coordinance numberq. For regular
lattices, q reduces to the usual coordination number while for anisotropic
lattices it is an effective coordination number. For dynamical percolation we
conjecture that the law is still valid if we use the number q_2 of second
nearest neighbors instead of q. This conjecture is checked for the dynamic
epidemic model which considers the percolation phenomenon in a mobile
disordered system. The agreement is good.Comment: 8 pages, latex, 3 figures include
On Uzbek converb constructions expressing motion events
Converbs, which are widely used in Turkic languages, constitute a number of converb constructions conveying aspectual and Aktionsart meanings. These constructions, often called 'auxiliary verb constructions', have been well studied. In this article, however, which is restricted to Uzbek, we will study in detail a different kind of converb construction, that until today mainly went unnoticed by turcologists: the 'converb construction of motion' (CCM). It is defined as a succession of verbs, linked with the converb suffix -(i)b, in which each verb expresses a separate semantic component of the same motion event. Our research based on a monolingual Uzbek corpus showed that three Main Types and one Extra Type can be distinguished. These are made up of verbs belonging to well-defined semantic verbal categories, combinations of which constitute specific subtypes. It can be concluded that Uzbek has an elaborate system of CCMs
Dynamical analysis of S&P500 momentum
The dynamics of the S&P500 price signal is studied using a moving average
technique. Particular attention is paid to intersections of two moving averages
with different time horizons. The distributions of the slopes and angle between
two moving averages at intersections is analyzed, as well as that of the
waiting times between intersections. In addition, the distribution of maxima
and minima in the moving average signal is investigated. In all cases,
persistent patterns are observed in these probability measures and it is
suggested that such variables be considered for better analysis and possible
prediction of the trends of the signal.Comment: 17 pages, 9 figures; to be published in Physica
Origin of Crashes in 3 US stock markets: Shocks and Bubbles
This paper presents an exclusive classification of the largest crashes in Dow
Jones Industrial Average (DJIA), SP500 and NASDAQ in the past century. Crashes
are objectively defined as the top-rank filtered drawdowns (loss from the last
local maximum to the next local minimum disregarding noise fluctuations), where
the size of the filter is determined by the historical volatility of the index.
It is shown that {\it all} crashes can be linked to either an external shock,
{\it e.g.}, outbreak of war, {\it or} a log-periodic power law (LPPL) bubble
with an empirically well-defined complex value of the exponent. Conversely,
with one sole exception {\it all} previously identified LPPL bubbles are
followed by a top-rank drawdown. As a consequence, the analysis presented
suggest a one-to-one correspondence between market crashes defined as top-rank
filtered drawdowns on one hand and surprising news and LPPL bubbles on the
other. We attribute this correspondence to the Efficient Market Hypothesis
effective on two quite different time scales depending on whether the market
instability the crash represent is internally or externally generated.Comment: 7 pages including 3 tables and 3 figures. Subm. for Proceeding of
Frontier Science 200
Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case
The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary differential equations obtained by spatial finite-element discretisation of linear parabolic initial-boundary value problems. The results are compared to the corresponding continuous-time results. The theory is illustrated for a one-dimensional and a two-dimensional model problem and checked against results obtained by numerical experiments
Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method
This paper addresses optimization problems constrained by partial
differential equations with uncertain coefficients. In particular, the robust
control problem and the average control problem are considered for a tracking
type cost functional with an additional penalty on the variance of the state.
The expressions for the gradient and Hessian corresponding to either problem
contain expected value operators. Due to the large number of uncertainties
considered in our model, we suggest to evaluate these expectations using a
multilevel Monte Carlo (MLMC) method. Under mild assumptions, it is shown that
this results in the gradient and Hessian corresponding to the MLMC estimator of
the original cost functional. Furthermore, we show that the use of certain
correlated samples yields a reduction in the total number of samples required.
Two optimization methods are investigated: the nonlinear conjugate gradient
method and the Newton method. For both, a specific algorithm is provided that
dynamically decides which and how many samples should be taken in each
iteration. The cost of the optimization up to some specified tolerance
is shown to be proportional to the cost of a gradient evaluation with requested
root mean square error . The algorithms are tested on a model elliptic
diffusion problem with lognormal diffusion coefficient. An additional nonlinear
term is also considered.Comment: This work was presented at the IMG 2016 conference (Dec 5 - Dec 9,
2016), at the Copper Mountain conference (Mar 26 - Mar 30, 2017), and at the
FrontUQ conference (Sept 5 - Sept 8, 2017
Labyrinthic granular landscapes
We have numerically studied a model of granular landscape eroded by wind. We
show the appearance of labyrinthic patterns when the wind orientation turns by
. The occurence of such structures are discussed. Morever, we
introduce the density of ``defects'' as the dynamic parameter governing
the landscape evolution. A power law behavior of is found as a function
of time. In the case of wind variations, the exponent (drastically) shifts from
2 to 1. The presence of two asymptotic values of implies the
irreversibility of the labyrinthic formation process.Comment: 3 pages, 3 figure, RevTe
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