Entropy of seismic electric signals: Analysis in natural time under time-reversal

Electric signals have been recently recorded at the Earth's surface with amplitudes appreciably larger than those hitherto reported. Their entropy in natural time is smaller than that, $S_u$, of a ``uniform'' distribution. The same holds for their entropy upon time-reversal. This behavior, as supported by numerical simulations in fBm time series and in an on-off intermittency model, stems from infinitely ranged long range temporal correlations and hence these signals are probably Seismic Electric Signals (critical dynamics). The entropy fluctuations are found to increase upon approaching bursting, which reminds the behavior identifying sudden cardiac death individuals when analysing their electrocardiograms.Comment: 7 pages, 4 figures, copy of the revised version submitted to Physical Review Letters on June 29,200

Mandelbrot's stochastic time series models

I survey and illustrate the main time series models that Mandelbrot introduced into time series analysis in the 1960s and 1970s. I focus particularly on the members of the additive fractional stable family including Lévy flights and fractional Brownian motion (fBm), noting some of the less well‐known aspects of this family, such as the cases when the self‐similarity exponent H and the Hurst exponent J differ. I briefly discuss the role of multiplicative models in modeling the physics of cascades. I then recount the still little‐known story of Mandelbrot's work on fractional renewal models in the late 1960s, explaining how these differ from their more familiar fBm counterpart and form a “missing link” between fBm and the problem of random change points. I conclude by highlighting the frontier problem of damped fractional models

1/f Noise and Extreme Value Statistics

We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary conditions are periodic. We provide a realistic example of periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.Comment: 4 pages, 4 postscript figures, RevTe

Dynamical model and nonextensive statistical mechanics of a market index on large time windows

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbulent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a $\chi^2$-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at $ca.$ a 200 day time lag. The intermittency exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of $\kappa$ points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating ''no restoring force''. A comparison is made between normalized log-returns and mere price increments.Comment: 40 pages, 14 figures; accepted for publication in Phys Rev

On the simple random-walk models of ion-channel gate dynamics reflecting long-term memory

Several approaches to ion-channel gating modelling have been proposed. Although many models describe the dwell-time distributions correctly, they are incapable of predicting and explaining the long-term correlations between the lengths of adjacent openings and closings of a channel. In this paper we propose two simple random-walk models of the gating dynamics of voltage and Ca2+-activated potassium channels which qualitatively reproduce the dwell-time distributions, and describe the experimentally observed long-term memory quite well. Biological interpretation of both models is presented. In particular, the origin of the correlations is associated with fluctuations of channel mass density. The long-term memory effect, as measured by Hurst R/S analysis of experimental single-channel patch-clamp recordings, is close to the behaviour predicted by our models. The flexibility of the models enables their use as templates for other types of ion channel

Roughness distributions for 1/f^alpha signals

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions, distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also non-periodic signals on short intervals embedded in the full period. We find that for alpha=<1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for alpha>1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha=2 and alpha->infinity. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f^alpha processes.Comment: 12 pages incl. 6 figures, with RevTex4, for A4 paper, in v2 some references were correcte

Influence of fertilization on yield of crops and on soil environment

According to many publications, plant production should be on the level of 18 grain units per 1 statistical person. Taking into consideration requirements for food on the above level for 40 miln. of Polish citizens and 18.2 million of agricultural land, it is necessary to obtain average yield in Poland on the level of 38 grain units per hectare. Plant production on the above level is rather different to obtain because about 60% of arable soils in Poland are very acid with low magnesium content. Therefore we should increase the rates of lime and dolomite to obtain soil pH on the level of 5-6 as well as apply 170-180 kg NPK per ha

Działanie azotu na plonowanie roślin w zależności od odczynu gleby oraz nawożenia obornikiem

At the Experimental Station of the Agriculture and Biology Department of Warsaw University of Life Sciences in Skierniewice fertilization experiments have been carried out continuously since 1923, in which the effects of lime, nitrogen, phosphorus, potassium and farmyard manure are studied in a static system with rotation of a few crops. Farmyard manure has been applied on a very acidic soil with a pH of about 4, and on a slightly acidic soil with a pH of 6.0–6.5. This paper describes only the results from combinations with and without nitrogen fertilization in the fields without FYM (since 1923) and with FYM (since 1992). The results presented here include the mean for 4 years yields of potatoes (fertilized with FYM) and grain crops grown in successive years following farmyard manure applications. Included are also the most important properties of the soils sampled in the last year after treatments with farmyard manure. Yield increases resulting from nitrogen fertilization were very high and generally higher in the fields without manure than those with manure. The presence of farmyard manure was found to increase the organic carbon content and total nitrogen content in the soil by about 10 %. This type of fertilizer caused higher increases in yield in the combinations without nitrogen fertilization than in those involving applications of nitrogen.W Stacji Doświadczalnej Wydziału Rolnictwa i Biologii SGGW w Skierniewicach nieprzerwanie od 1923 r. prowadzone są doświadczenia nawozowe, gdzie bada się działanie wapna, azotu, fosforu, potasu i obornika w układzie statycznym w kilku zmianowaniach roślin. Obornik stosuje się na glebie bardzo kwaśnej o pH około 4 oraz słabo kwaśnej o pH 6,0-6,5. W niniejszej pracy zamieszczono wyniki badań uzyskane tylko z obiektów nawożonych i nienawożonych azotem, na polach bez obornika (od 1923 r.) i z obornikiem (od 1992 r.). Uzyskane dane obejmują średnie z 4 lat plony ziemniaków (nawożonych obornikiem) oraz plony roślin zbożowych uprawianych w kolejnych latach po oborniku. Zamieszczono również najważniejsze właściwości gleb pobranych w ostatnim roku po oborniku. Zwyżki plonów pod wpływem nawożenia azotem były bardzo duże i przeważnie większe na polach bez obornika niż z obornikiem. Obornik zwiększał zawartość węgla organicznego i azotu ogólnego w glebie o około 10 %. Nawóz ten bardziej zwiększał plony na obiektach nienawożonych azotem niż na kombinacjach, gdzie stosowano ten składnik

Wplyw wegla brunatnego, torfu oraz slomy na dostepnosc pierwiastkow sladowych dla roslin

Badania prowadzono metodą doświadczeń laboratoryjnych, wazonowych i polowych. W doświadczeniu laboratoryjnym badano, przy użyciu kolumn glebowych (6 x 40 cm), mobilność Zn, Cd, Pb i Cu w glebie w zależności od dodatku słomy jęczmiennej oraz zróżnicowanego pH gleby (5,4: 6,2; 7,0). W doświadczeniu wazonowym i polowym badano natomiast pobieranie Zn, Cd i Pb przez rośliny uprawne w zależności od zastosowania trzech rodzajów materii organicznej: słomy, torfu i węgla brunatnego. Badania prowadzono na glebie silnie zanieczyszczonej Zn, Cd i Pb oraz o podwyższonej zawartości tych pierwiastków. Roślinami testowymi w doświadczeniu wazonowym i polowym były: burak ćwikłowy, sałata, żyto, jęczmień jary, ziemniak oraz pszenżyto jare. W doświadczeniu modelowym stwierdzono, że dodatek słomy zmniejszał ruchliwość cynku i kadmu w glebie kwaśnej, natomiast zwiększał mobilność ołowiu i miedzi w glebie kwaśnej i lekko kwaśnej. Dodatek słomy do gleby zwiększał również bioakumulację Pb w doświadczeniu wazonowym. Spośród badanych trzech rodzajów substancji organicznej, węgiel brunatny wykazywał najlepszą skuteczność w ograniczaniu pobierania Zn, Cd i Pb przez rośliny.The research was conducted under laboratory, green house and field conditions. In the laboratory experiment, the solubility of Zn, Cd, Pb and Cu depending on application of barley straw and soil pH (5.4; 6.2; 7.0), was estimated by using soil columns. Columns (6 x 40 cm) were filled with loam sand soil contaminated with those elements. The uptake of Zn, Cd and Pb by plants from two soils (with higher and lower heavy metals contamination) depending on the application of brown coal, peat and straw was studied in the green house and field experiments. Red beet, lettuce, rye, spring barley, potato and triticale were grown in pots and on the field. Application of straw decreased the solubility of Zn and Cd, but increased the solubility of Pb and Cu in acidic soil. Straw increased uptake of Pb by plants in the pot experiment, too. Brown coal mostly limited the uptake of Zn, Cd and Pb by plants, as compared with peat and straw