Exit probability in a one-dimensional nonlinear q-voter model

We formulate and investigate the nonlinear $q$-voter model (which as special cases includes the linear voter and the Sznajd model) on a one dimensional lattice. We derive analytical formula for the exit probability and show that it agrees perfectly with Monte Carlo simulations. The puzzle, that we deal with here, may be contained in a simple question: "Why the mean field approach gives the exact formula for the exit probability in the one-dimensional nonlinear $q$-voter model?". To answer this question we test several hypothesis proposed recently for the Sznajd model, including the finite size effects, the influence of the range of interactions and the importance of the initial step of the evolution. On the one hand, our work is part of a trend of the current debate on the form of the exit probability in the one-dimensional Sznajd model but on the other hand, it concerns the much broader problem of nonlinear $q$-voter model

Some new results on one-dimensional outflow dynamics

In this paper we introduce modified version of one-dimensional outflow dynamics (known as a Sznajd model) which simplifies the analytical treatment. We show that simulations results of the original and modified rules are exactly the same for various initial conditions. We obtain the analytical formula for exit probability using Kirkwood approximation and we show that it agrees perfectly with computer simulations in case of random initial conditions. Moreover, we compare our results with earlier analytical calculations obtained from renormalization group and from general sequential probabilistic frame introduced by Galam. Using computer simulations we investigate the time evolution of several correlation functions to show if Kirkwood approximation can be justified. Surprisingly, it occurs that Kirkwood approximation gives correct results even for these initial conditions for which it cannot be easily justified.Comment: 6 pages, 7 figure

The absolute chronology of collective burials from the 2nd Millennium BC in East Central Europe

This article discusses the absolute chronology of collective burials of the Trzciniec Cultural Circle communities of the Middle Bronze Age in East Central Europe. Based on Bayesian modeling of 91 accelerator mass spectrometry radiocarbon (AMS 14C) dates from 18 cemeteries, the practice of collective burying of individuals was linked to a period of 400-640 (95.4%) years, between 1830–1690 (95.4%) and 1320-1160 (95.4%) BC. Collective burials in mounds with both cremation and inhumation rites were found earliest in the upland zone regardless of grave structure type (mounded or flat). Bayesian modeling of 14C determinations suggests that this practice was being transmitted generally from the southeast to the northwest direction. Bayesian modeling of the dates from the largest cemetery in Z· erniki Górne, Lesser Poland Upland, confirmed the duration of use of the necropolis as ca. 140–310 (95.4%) years. Further results show the partial contemporaneity of burials and allow formulation of a spatial and temporal development model of the necropolis. Based on the investigation, some graves were used over just a couple of years and others over nearly 200, with up to 30 individuals found in a single grave

Population genomics of post-glacial western Eurasia.

Western Eurasia witnessed several large-scale human migrations during the Holocene <sup>1-5</sup> . Here, to investigate the cross-continental effects of these migrations, we shotgun-sequenced 317 genomes-mainly from the Mesolithic and Neolithic periods-from across northern and western Eurasia. These were imputed alongside published data to obtain diploid genotypes from more than 1,600 ancient humans. Our analyses revealed a 'great divide' genomic boundary extending from the Black Sea to the Baltic. Mesolithic hunter-gatherers were highly genetically differentiated east and west of this zone, and the effect of the neolithization was equally disparate. Large-scale ancestry shifts occurred in the west as farming was introduced, including near-total replacement of hunter-gatherers in many areas, whereas no substantial ancestry shifts happened east of the zone during the same period. Similarly, relatedness decreased in the west from the Neolithic transition onwards, whereas, east of the Urals, relatedness remained high until around 4,000 BP, consistent with the persistence of localized groups of hunter-gatherers. The boundary dissolved when Yamnaya-related ancestry spread across western Eurasia around 5,000 BP, resulting in a second major turnover that reached most parts of Europe within a 1,000-year span. The genetic origin and fate of the Yamnaya have remained elusive, but we show that hunter-gatherers from the Middle Don region contributed ancestry to them. Yamnaya groups later admixed with individuals associated with the Globular Amphora culture before expanding into Europe. Similar turnovers occurred in western Siberia, where we report new genomic data from a 'Neolithic steppe' cline spanning the Siberian forest steppe to Lake Baikal. These prehistoric migrations had profound and lasting effects on the genetic diversity of Eurasian populations

Hybrid fuzzy clustering method

A new hybrid clustering method based on a fuzzy myriad is presented. The proposed method could be considered as a generalisation of the well known fuzzy c-means method (FCM) proposed by Bezdek. Existing modifications of the FCM method, such as conditional clustering or partial supervised clustering can be applied to determine the objective function of the proposed method

Breast cancer diagnosis via fuzzy clustering with partial supervision

A new clustering method of fuzzy c-myriad clustering with partial supervision is presented in this paper. The proposed method has been applied to breast cancer diagnosis data obtainted from the University of Wisconsin. The data set contains 699 cases of breast cancer, with each instance described by 10 features

An application of the Lp-norm in robust weighted averaging of biomedical signals

Averaging is one of the basic methods of statistical analysis of experimental data where the response of the system is periodic or quasi-periodic. As long as the noise are Gaussian, the standard averaging leads to good results and effective noise reduction. However, when the distortions have impulsive nature, then such an approach leads to a deterioration of the system. In this case the robust methods should be applied which are characterized by resistance to a statistical sample spoken. In this work a robust averaging method based on the minimization of a scalar criterion function using a Lp-norm functions are presented. The effectiveness of the proposed method was tested in an averaging periods aligned ECG signal cycles in the presence of impulse noise

Fuzzy clustering based methods for nystagmus movements detection in electronystagmography signal

The analysis of optokinetic nystagmus (OKN) provides valuable information about the condition of human vision system. One of the phenomena that is used in the medical diagnosis is optokinetic nystagmus. Nystagmus are voluntary or involuntarily eye movements being a response to a stimuli which activate the optokinetic systems. The electronystagmography (ENG) signal corresponding to the nystagmus has a form of a saw tooth waveform with fast components related to saccades. The accurate detection of the saccades in the ENG signal is the base for the further estimation of the nystagmus characteristic. The proposed algorithm is based on the proper filtering of the ENG signal providing a waveform with amplitude peaks corresponding the fast eyes rotation. The correct recognition of the local maxima of the signal is obtained by the means of fuzzy c-means clustering (FCM). The paper presents three variants of saccades detection algorithm based on the FCM. The performance of the procedures was investigated using the artificial as well as the real optokinetic nystagmus cycles. The proposed method provides high detection sensitivity and allows for the automatic and precise determination of the saccades location in the preprocessed ENG signal

Hybrid QRS detector based on dynamic reconfigurable field programmable analog array

W artykule zaprezentowano nową koncepcję układu detekcji w czasie rzeczywistym zespołu QRS z przebiegu elektrokardiograficzngo. W detektorze wykorzystano programowalną matrycę analogową AN221E04 firmy Anadigm. Parametry wybranych bloków są na bieżąco zmieniane w zależności od zmian parametrów przebiegu EKG dzięki dynamicznej rekonfigurowalności układu. Uzyskano bardzo krótki czas reakcji detektora na wykryty zespół QRS przy zadowalającej skuteczności detekcji. Opracowany detektor może znaleźć zastosowanie w aplikacjach biomedycznych wymagających wykrywania zespołu QRS w przebiegu EKG z małym opóźnieniem czasowym.In many applications it is important to detect the QRS complex in the ECG waveform with possibly low time delay. Traditional software detectors of the QRS complex implement algorithms, usually based on cascades of digital filters, introduce delays up to parts of a second. Hardware QRS detectors (Fig. 1) fulfill the low delay requirements, but have worse adaptive features for the changing ECG shape. In this paper a new approach to QRS detection is presented. The proposed solution implements a classical detector structure in a Field Programmable Analog Array (FPAA) i.e. AN221E04 circuit from the AnadigmŽ company - Fig. 3. The most interesting feature of the FPAA is the dynamic reconfigurability. This solution makes it possible to modify the parameters of particular blocks of the detector or even the whole structure during runtime, without any changes in hardware and disturbance of the system functionality. Important parameters of particular blocks of the QRS detector are modified on-the-fly according to changes observed in the ECG signal. New data are calculated by the AD7020 microcontroller and downloaded to the FPAA using dynamic reconfigurability after each QRS detection. The prototype QRS detector was tested using a real ECG signal taken from Mit-Bih Arrythmia Database. The results obtained in the prototype circuit (Table 1) show that the detection delay is really small. The error rate of the QRS detection is low and can be acceptable in most real time applications