The ability to discriminate relative and absolute number has been researched widely in both human and nonhuman species. However, the full extent of numerical ability in nonhuman animals, and the nature of the underlying numerical representation, on which discriminations are based, is still unclear. The aim of the current research was to examine the performance of pigeons and humans in tasks that require the discrimination of relative number (a bisection procedure), and absolute number (in a reproduction procedure). One of the main research questions was whether numerical control over responding could be obtained, above and beyond control by temporal cues in nonhuman animals, and if so, whether it was possible to quantify the relative influences of number and time on responding. Experiment 1 examines nonhuman performance in a numerical bisection task; subjects were presented with either 2 and 6, 4 and 12, or 8 and 24 keylight flashes across three different conditions, and were required to classify these flash sequences as either a “large” or “small” number, by pecking the blue or white key, respectively. Subjects were then tested with novel values within and 2 values higher and lower than the training values. Experiments 2-4 investigate responding in a novel numerical reproduction procedure, in which pigeons were trained to match the number of responses made during a production phase to the number of keylight flashes (2, 4, or 6) in a recently completed sample phase. Experiments 2 and 2A examined discrimination performance when the temporal variables, flash rate and sample phase duration, were perfectly correlated (Experiment 2) or only weakly correlated (Experiment 2a) with flash number. Acquisition of performance in the numerical reproduction procedure was investigated in Experiment 3. For Experiments 1-3, hierarchical regression analyses showed significant control by number over responding, after controlling for temporal cues. Additionally, positive transfer to novel values both within and outside the training range was obtained when the temporal organization of test sequences was similar to baseline training. Experiment 4 investigated the effects of increasing or decreasing the retention interval (RI) on performance in the reproduction procedure, and found this produced a response bias towards larger numbers, contrary to predictions based on previous RI research, and suggested responding was not affected by memorial decay processes. The structure of the representation of number developed by subjects in the bisection and reproduction procedures was investigated using analyses of responding and response variability in Chapters 2 and 6, respectively. Bisection points obtained in Experiment 1 were located at the arithmetic, not geometric mean of all three scales, and coefficients of variation (CVs) obtained in both the bisection and reproduction experiments tended to decrease as flash number increased. Additionally, analyses of the acquisition data found differences in average response number was better fit by a linear than logarithmic scale. These results show that responding did not conform to scalar variability and is largely inconsistent with previous nonhuman research. Together these results suggest responding appeared to be based on a linear scale of number with constant generalisation between values, similar to that associated with human verbal counting, rather than a logarithmic scale with constant generalisation or a linear scale with scalar generalisation between values. Experiment 5 compared pigeons’ and humans’ verbal and nonverbal discrimination performance with numbers 1-20 in analogous bisection, reproduction and report tasks. Human verbal and nonverbal performance in the three tasks was similar and resembled nonhuman performance, although verbal discriminations were more accurate and less variable. The main findings from Experiments 1 and 2A were replicated with humans; bisection points were located at the arithmetic mean, average response number increased linearly as sample number increased, though there was a tendency to underestimate sample number, and decreasing CVs were also obtained for values less than 8. An additional, interesting finding was that CVs showed scalar variability for values greater than 8, suggesting a less exact representation and discrimination process was being used for these values. Collectively, these five experiments provide new evidence for a nonverbal ability to discriminate relative and absolute number with increasing relative accuracy resembling human verbal counting in both human and nonhumans.

Modification of DNA sequences and their suitable representation is important part of analysis, comparison and another processing. Goal of this paper is finding of suitable methods for representation of genomic and proteomic sequences. Because there is great number of metods, this paper will introduce only some of them. All selected methods, are described in the first part of this paper and they were programed in Matlab. Selected methods are illustrated on coding sequences of the first exon of the b-globin gene of 11 different species. Results are compared withresults from the original papers. Some methods are capable of another processing like cluster analysis. Output of this paper is comparison of results, gained from different methods, and finding the most suitable one.

This thesis discusses about possibilities of construction colour DNA spectrograms and about patterns which can be detected there. Spectrograms as tools of spectral analysis give us a simultaneous view of the local frequency throughout the nucleotide sequence. They are suitable for gene identification or gene regions identification, determination of global character about whole chromosomes and also give us a chance for the discovery of yet unknown regions of potential significance. For purpose of this kind of DNA analysis is possible to use digital signal processing methods. We can apply them on only after conversion of DNA sequence to numerical representation. Selection of correct numerical representation affects how well will be reflected biological features in numerical record which we need for another use in digital signal analysis.

Mobile genetic elements are occupied by this project. It is aimed at their features, which can be used for their detection. It also deals with issue of conversion of symbolic sequence into numerical form. Classifications of mobile genetic elements are explained, basic types of mobile genetic sequences are described, and principles of numerical maps and detection in symbolic represetation are also clarified. Conversion of symbolic genetical sequences by chosen numerical map and calculation of normalized correlation values for set of mobile genetic elements are compiled. Analysis of the mobile genetic elements properties is performed for design of detector. The library of themes is created at the end for usage by designed detector.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Esta pesquisa analisa os saberes docentes e os conhecimentos discentes do 3 ano do Ensino Fundamental sobre o sistema de numeraÃÃo decimal â SND. A HistÃria do SND, de acordo com Ifrah (2005) e Eves (2011), permite conhecer o desenvolvimento das suas caracterÃsticas â as bases, os algarismos, a criaÃÃo do zero â o que favorece uma EducaÃÃo MatemÃtica problematizadora. Os objetivos dessa pesquisa, que à um estudo de caso, sÃo: i) identificar os conhecimentos de estudantes do 3 ano do Ensino Fundamental na escrita de nÃmeros, com 2 e 3 ordens, e os saberes docentes mobilizados na interpretaÃÃo de tais registros; ii) conhecer registros de representaÃÃo de estudantes do 3 ano do Ensino Fundamental na escrita de nÃmeros, com 2 e 3 ordens; e iii) investigar como a professora analisa as escritas discentes de nÃmeros, com 2 e 3 ordens, em diferentes registros de representaÃÃo. Participaram da pesquisa 24 estudantes do 3 ano do Ensino Fundamental e uma professora de uma escola pÃblica do municÃpio de Maranguape, regiÃo Metropolitana de Fortaleza. Os saberes discentes foram avaliados nos seguintes aspectos: ComparaÃÃo de numerais com quantidade diferente de algarismos; ComparaÃÃo de numerais com a mesma quantidade de algarismos; Do numeral verbal falado para o numeral arÃbico (escrever); Do numeral verbal falado para o numeral arÃbico (escolher uma opÃÃo); Do numeral arÃbico para numeral verbal escrito (por extenso); Do numeral escrito (por extenso) para o numeral arÃbico. As questÃes foram organizadas em itens que continham numerais com 2, 3 e 4 algarismos. ApÃs a aplicaÃÃo do teste, realizou-se com a professora regente uma entrevista estruturada dividida em 3 momentos: o primeiro, relacionado aos seus saberes do conhecimento, pedagÃgicos e existenciais sobre o SND; o segundo, com perguntas com o objetivo de compreender como esta analisa as produÃÃes dos seus estudantes; e o terceiro, abordando as reflexÃes da professora sobre a pesquisa realizada. Os resultados com os estudantes revelaram a necessidade do trabalho com as diversas representaÃÃes do SND e o fato que mais da metade dos estudantes jà possui algum conceito sobre a quarta ordem do SND, mesmo sem esse conteÃdo constar do currÃculo referente ao seu ano e nÃo ter sido estudado, ratificando outros estudos os quais afirmam que os estudantes estÃo na escola com aprendizagens que esta nÃo os proporcionou. O currÃculo, portanto, precisa ser revisto, pois o engessamento de alguns conteÃdos a determinado momento restringe a aprendizagem dos estudantes. Os resultados com a professora evidenciam uma prÃtica que tem no livro didÃtico seu principal recurso metodolÃgico e desconhecimento das caracterÃsticas do SND. Ratifica-se, dessa forma, a necessidade de uma formaÃÃo docente dessa etapa da escolarizaÃÃo que englobe todos os saberes do conhecimento. Espero que este estudo contribua para novas pesquisas, favorecendo o desenvolvimento de uma EducaÃÃo MatemÃtica que as crianÃas merecem para uma vida mais plena.

This dissertation deals with alternative techniques for analysis of genetic information of organisms. The theoretical part presents two different approaches for evaluation of relationship between organisms based on mutual similarity of genetic information contained in their DNA sequences. The first approach is currently standardized phylogenetics analysis of character based records of DNA sequences. Although this approach is computationally expensive due to the need of multiple sequence alignment, it allows evaluation of global and local similarity of DNA sequences. The second approach is represented by techniques for classification of DNA sequences in a form of numerical vectors representing characteristic features of their genetic information. These methods known as „alignment free“ allow fast evaluation of global similarity but cannot evaluate local changes. The new method presented in this dissertation combines the advantages of both approaches. It utilizes numerical representation similar to 1D digital signal, i.e. representation that contains specific trend along x-axis. The experimental part of dissertation deals with design of a set of appropriate tools for genomic signal processing to allow evaluation mutual similarity of taxonomically specific trends. On the basis of the mutual similarity of genomic signals, the classification in the form of dendrogram is applied. It corresponds to phylogenetic trees used in standard phylogenetics.

Numerical cognition has been shown to share many aspects of spatial cognition, both behavioural and neurological. However, it is unclear whether a particular type of spatial cognition, visuospatial mental imagery (VSMI), may play a role in symbolic numerical representation. In this thesis, I first show that mental rotation, a form of VSMI, is related to two measures of basic numerical representation. I then show that number-space synaesthesia (NSS), a rare type of VSMI involving visualised spatial layouts for numbers, does not show an advantage in mental rotation, but shows interference in number line mapping. I next present a study investigating links between NSS and the ability to learn novel numerical symbols. I demonstrate that NSS shows an advantage at learning novel numerals, and that transcranial random noise stimulation, which increases cortical excitability, confers broadly similar advantages that nonetheless differ in subtle ways. I present a study of transcranial alternating current stimulation on the same symbol learning paradigm, which fails to demonstrate effects. Lastly, I present data showing that strength of numerical representation in these newly-learnt symbols is correlated with a measure of mental rotation, and also with visual recognition ability for the symbols after, but not before, training. All together, these findings suggest that VSMI does indeed play a role in numerical cognition, and that it may do so from an early stage of learning symbolic numbers.