241 research outputs found
Attractors and basins of dynamical systems
There are several programs for studying dynamical systems, but none of them is very useful for investigating basins and attractors of higher dimensional systems. Our goal in this paper is to show a new algorithm for finding even chaotic attractors and their basins for these systems. We present an implementation and examples for the use of this program
Az emberi agy számreprezentációs készségének normál és sérült funkciója és fejlődése = Neurocognitive study of normal and impaired function and development of human numerical representations
Kutatásunkban a matematikai kĂ©pessĂ©gek normál Ă©s sĂ©rĂĽlt funkciĂłját vizsgáltuk viselkedĂ©ses Ă©s esemĂ©nyhez-kötött kiváltott potenciál (EKP) mĂłdszerrel. Kutatási eredmĂ©nyeinkbĹ‘l öt nemzetközi lektorált publikáciĂł szĂĽletett (Neuropsychologia, BMC Behavioral and Brain Functions, Neuroscience Letters [2], Mind, Brain and Education), kĂ©t további publikáciĂł jelenleg lektorálás alatt áll (Journal of Experimental Child Psychology, Behavioral and Brain Sciences). Sikeresen azonosĂtottuk az automatikus matematikai informáciĂłfeldolgozás EKP jellemzĹ‘it felnĹ‘ttekben Ă©s 6-11 Ă©ves gyermekekben. MegállapĂtottuk, hogy a matematikai feldolgozás automatikus voltát mĂ©rĹ‘ feladatokban a motoros folyamatok Ă©retlensĂ©ge jelentĹ‘s mĂ©rtĂ©kben hozzájárul ahhoz, hogy gyermekek rosszabb teljesĂtmĂ©nyt mutatnak, mint felnĹ‘ttek. Diszkalkuliásokkal vĂ©gzett vizsgálataink kimutatták, hogy a jelenleg domináns, a nagyság-reprezentáciĂł sĂ©rĂĽlt voltát feltĂ©telezĹ‘ elmĂ©letek nem kĂ©pesek megmagyarázni a diszkalkulia jelensĂ©gĂ©t. Vizsgálatunk ezzel szemben azt mutatta, hogy a figyelmi folyamatok Ă©retlensĂ©ge jelentĹ‘s tĂ©nyezĹ‘ lehet a matematikai kĂ©pessĂ©gzavarokban. Egy közel száz Ăłvodáson vĂ©gzett kutatásunk szintĂ©n arra utal, hogy a nagyságreprezentáciĂł fejlĹ‘dĂ©se nem kĂ©pes megmagyarázni a matematikai kĂ©pessĂ©gek fejlĹ‘dĂ©sĂ©t. EredmĂ©nyeink jelentĹ‘sek, mivel a jelenlegi elmĂ©leti keretek Ăşjragondolására kĂ©sztetnek. A motoros Ă©s figyelmi folyamatok sĂ©rĂĽlĂ©sĂ©re mutatĂł eredmĂ©nyeink kijelölik a további kutatás irányát. | Our research investigated normal and impaired function of arithmetic abilities by using behavioral methods and event-related brain potentials (ERPs). We have published five papers in international peer-reviewed journals (Neuropsychologia, BMC Behavioral and Brain Functions, Neuroscience Letters [2], Mind, Brain and Education). Two more papers are currently under review (Journal of Experimental Child Psychology, Behavioral and Brain Sciences). We have identified ERP markers of automatic number processing in adults and in 6-11-year-old children. We have established that the immaturity of motor processes contributes crucially to worse performance of children than adults? in tasks measuring automatic number processing. Studies of dyscalculia demonstrated that the currently dominant theory assuming that the number representation is impaired in dyscalculia cannot explain the phenomenon clearly. Our investigations suggest that immature attentional function probably plays a major role in the aetiology of dyscalculia. An investigation of about 100 kindergarten children also confirmed that the development of the magnitude representation is probably not the major underlying factor behind numerical development. Results are significant because they prompt a rethink of the current theoretical stance on number cognition. Our data demonstrating impairments of motor and attentional function in dyscalculia shows the pathway of further research
Neimark-sacker bifurcation in a discrete dynamical model of population genetics
In this paper we investigate a genetic model initiated by Gábor Tusnády. This model is a four-dimensional system of difference equations which describes the change of distribution of genotypes from generation to generation in the case of one locus and four alleles considering selection and mutation. During computer experiments Tusnády discovered cyclic behaviour in the evolution of genotypes. Using bifurcation theory we prove that the system indeed can have cycles and this occurrence is caused by a Neimark-Sacker bifurcation
A Mathematical Model for Zika Virus Infection and Microcephaly Risk Considering Sexual and Vertical Transmission
We establish a compartmental model for Zika virus disease transmission, with particular attention paid to microcephaly, the main threat of the disease. To this end, we consider separate microcephaly-related compartments for affected infants, as well as the role of asymptomatic carriers, the influence of seasonality and transmission through sexual contact. We determine the basic reproduction number of the corresponding time-dependent model and time-constant model and study the dependence of this value on the mosquito-related parameters. In addition, we demonstrate the global stability of the disease-free periodic solution if R01. We fit our model to data from Colombia between 2015 and 2017 as a case study. The fitting is used to figure out how sexual transmission affects the number of cases among women as well as the number of microcephaly cases. Our sensitivity analyses conclude that the most effective ways to prevent Zika-related microcephaly cases are preventing mosquito bites and controlling mosquito populations, as well as providing protection during sexual contact
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