On Max-Stable Processes and the Functional D-Norm

We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. The distribution function G of a continuous max-stable process on [0,1] is introduced and it is shown that G can be represented via a norm on functional space, called D-norm. This is in complete accordance with the multivariate case and leads to the definition of functional generalized Pareto distributions (GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete accordance with the uni- or multivariate case. Applying this framework to copula processes we derive characterizations of the domain of attraction condition for copula processes in terms of tail equivalence with a functional GPD. \delta-neighborhoods of a functional GPD are introduced and it is shown that these are characterized by a polynomial rate of convergence of functional extremes, which is well-known in the multivariate case.Comment: 22 page

Сучасний стан пенсійного забезпечення в Україні

У статті розглянуто сучасний стан солідарної системи загальнообов'язкового державного пенсійного страхування та проаналізовано основні показники функціонування недержавних пенсійних фондів.In the article the current state of solidarity system of obligatory slate pension insurance is considered. The basic indicators of functioning of non-stale pension funds are analyzed

Extreme value statistics and return intervals in long-range correlated uniform deviates

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to minimum are such that the reference point from which the maximum is measured is itself a random quantity. We analytically calculate the limiting distributions for independent and identically distributed random variables, and use these as a reference point for correlated cases. The distributions are different from that of the maximum itself i.e., a Weibull distribution, reflecting the fact that the distribution of the reference point either dominates over or convolves with the distribution of the maximum. The functional form of the limiting distributions is unaffected by correlations, although the convergence is slower. We show that our findings can be directly generalized to a wide class of stochastic processes. We also analyze return interval distributions, and compare them to recent conjectures of their functional form

Minimalist AdaBoost for blemish identification in potatoes

We present a multi-class solution based on minimalist Ad- aBoost for identifying blemishes present in visual images of potatoes. Using training examples we use Real AdaBoost to rst reduce the fea- ture set by selecting ve features for each class, then train binary clas- siers for each class, classifying each testing example according to the binary classier with the highest certainty. Against hand-drawn ground truth data we achieve a pixel match of 83% accuracy in white potatoes and 82% in red potatoes. For the task of identifying which blemishes are present in each potato within typical industry dened criteria (10% coverage) we achieve accuracy rates of 93% and 94%, respectively

A method for mechanical generation of radio frequency fields in nuclear magnetic resonance force microscopy

We present an innovative method for magnetic resonance force microscopy (MRFM) with ultra-low dissipation, by using the higher modes of the mechanical detector as radio frequency (rf) source. This method allows MRFM on samples without the need to be close to an rf source. Furthermore, since rf sources require currents that give dissipation, our method enables nuclear magnetic resonance experiments at ultra-low temperatures. Removing the need for an on-chip rf source is an important step towards a MRFM which can be widely used in condensed matter physics.Comment: 7 pages, 5 figures, to be submitted to Physical Review Applie

Multiplicative processes and power laws

[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We briefly explain the physical mechanism leading to a power law pdf and provide a list of references for these results dating back from a quarter of century. We explain how the formulation in terms of the characteristic function developed by Takayasu et al. can be extended to exponents $\mu >2$, which explains the ``reason of the lucky coincidence''. The multidimensional generalization of (\ref{eq1}) and the available results are briefly summarized. The discovery of stretched exponential tails in the presence of the cut-off introduced in \cite{Taka} is explained theoretically. We end by briefly listing applications.Comment: Extended version (7 pages). Phys. Rev. E (to appear April 1998

Extreme value distributions and Renormalization Group

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show, however, that more general rescalings are natural and lead to new limit distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The problem is approached using the language of Renormalization Group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of the differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections.Comment: 16 pages, 5 figures. Final versio

AMPT-induced monoamine depletion in humans: evaluation of two alternative [123I]IBZM SPECT procedures

Purpose Acute monoamine depletion paradigms using alpha-methyl-para-tyrosine (AMPT) combined with single photon emission computed tomography (SPECT) have been used successfully to evaluate disturbances in central dopaminergic neurotransmission. However, severe side effects due to relatively high doses (4,500 to 8,000 mg) of AMPT have been reasons for study withdrawal. Thus, we assessed the effectiveness and tolerability of two alternative procedures, using lower doses of AMPT. Methods Six healthy subjects underwent three measurements of striatal dopamine D2 receptor (D2R)-binding potential (BPND) with SPECT and the selective radiolabeled D2R antagonist [123I]IBZM. All subjects were scanned in the absence of pharmacological intervention (baseline) and after two different depletion procedures. In the first depletion session, over 6 h, subjects were administered 1,500 mg of AMPT before scanning. In the second depletion session, over 25 h, subjects were administered 40 mg AMPT/kg body weight. We also administered the Subjective Well-being Under Neuroleptic Treatment Scale, a self-report instrument designed to measure the subjective experience of patients on neuroleptic medication. Results We found no change of mean D2R BPND after the first and short AMPT challenge compared to the baseline. However, we found a significant increase in striatal D2R BPND binding after the AMPT challenge adjusted for bodyweight compared to both other regimen. Although subjective well-being worsened after the prolonged AMPT challenge, no severe side effects were reported. Conclusions Our results imply a low-dosage, suitable alternative to the common AMPT procedure. The probability of side effects and study withdrawal can be reduced by this procedure

Extreme fluctuations in noisy task-completion landscapes on scale-free networks

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.Comment: 16 pages, 6 figures, revte