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Mathematical modeling of biological phenomena has experienced increasing interest since new high-throughput technologies give access to growing amounts of molecular data. These modeling approaches are especially able to test hypotheses which are not yet experimentally accessible or guide an experimental setup. One particular attempt investigates the evolutionary dynamics responsible for today's composition of organisms. Computer simulations either propose an evolutionary mechanism and thus reproduce a recent finding or rebuild an evolutionary process in order to learn about its mechanism. The quest for evolutionary fingerprints in metabolic and gene-coexpression networks is the central topic of this cumulative thesis based on four published articles. An understanding of the actual origin of life will probably remain an insoluble problem. However, one can argue that after a first simple metabolism has evolved, the further evolution of metabolism occurred in parallel with the evolution of the sequences of the catalyzing enzymes. Indications of such a coevolution can be found when correlating the change in sequence between two enzymes with their distance on the metabolic network which is obtained from the KEGG database. We observe that there exists a small but significant correlation primarily on nearest neighbors. This indicates that enzymes catalyzing subsequent reactions tend to be descended from the same precursor. Since this correlation is relatively small one can at least assume that, if new enzymes are no "genetic children" of the previous enzymes, they certainly be descended from any of the already existing ones. Following this hypothesis, we introduce a model of enzyme-pathway coevolution. By iteratively adding enzymes, this model explores the metabolic network in a manner similar to diffusion. With implementation of an Gillespie-like algorithm we are able to introduce a tunable parameter that controls the weight of sequence similarity when choosing a new enzyme. Furthermore, this method also defines a time difference between successive evolutionary innovations in terms of a new enzyme. Overall, these simulations generate putative time-courses of the evolutionary walk on the metabolic network. By a time-series analysis, we find that the acquisition of new enzymes appears in bursts which are pronounced when the influence of the sequence similarity is higher. This behavior strongly resembles punctuated equilibrium which denotes the observation that new species tend to appear in bursts as well rather than in a gradual manner. Thus, our model helps to establish a better understanding of punctuated equilibrium giving a potential description at molecular level. From the time-courses we also extract a tentative order of new enzymes, metabolites, and even organisms. The consistence of this order with previous findings provides evidence for the validity of our approach. While the sequence of a gene is actually subject to mutations, its expression profile might also indirectly change through the evolutionary events in the cellular interplay. Gene coexpression data is simply accessible by microarray experiments and commonly illustrated using coexpression networks where genes are nodes and get linked once they show a significant coexpression. Since the large number of genes makes an illustration of the entire coexpression network difficult, clustering helps to show the network on a metalevel. Various clustering techniques already exist. However, we introduce a novel one which maintains control of the cluster sizes and thus assures proper visual inspection. An application of the method on Arabidopsis thaliana reveals that genes causing a severe phenotype often show a functional uniqueness in their network vicinity. This leads to 20 genes of so far unknown phenotype which are however suggested to be essential for plant growth. Of these, six indeed provoke such a severe phenotype, shown by mutant analysis. By an inspection of the degree distribution of the A.thaliana coexpression network, we identified two characteristics. The distribution deviates from the frequently observed power-law by a sharp truncation which follows after an over-representation of highly connected nodes. For a better understanding, we developed an evolutionary model which mimics the growth of a coexpression network by gene duplication which underlies a strong selection criterion, and slight mutational changes in the expression profile. Despite the simplicity of our assumption, we can reproduce the observed properties in A.thaliana as well as in E.coli and S.cerevisiae. The over-representation of high-degree nodes could be identified with mutually well connected genes of similar functional families: zinc fingers (PF00096), flagella, and ribosomes respectively. In conclusion, these four manuscripts demonstrate the usefulness of mathematical models and statistical tools as a source of new biological insight. While the clustering approach of gene coexpression data leads to the phenotypic characterization of so far unknown genes and thus supports genome annotation, our model approaches offer explanations for observed properties of the coexpression network and furthermore substantiate punctuated equilibrium as an evolutionary process by a deeper understanding of an underlying molecular mechanism.
It has recently been demonstrated that the presentation of a rare target in a visual oddball paradigm induces a prolonged inhibition of microsaccades. In the field of electrophysiology, the amplitude of the P300 component in event-related potentials (ERP) has been shown to be sensitive to the stimulus category (target vs. non target) of the eliciting stimulus, its overall probability, and the preceding stimulus sequence. In the present study we further specify the functional underpinnings of the prolonged microsaccadic inhibition in the visual oddball task, showing that the stimulus category, the frequency of a stimulus and the preceding stimulus sequence influence microsaccade rate. Furthermore, by co-recording ERPs and eye-movements, we were able to demonstrate that, despite being largely sensitive to the same experimental manipulation, the amplitude of P300 and the microsaccadic inhibition predict each other very weakly, and thus constitute two independent measures of the brain’s response to rare targets in the visual oddball paradigm.
Eye fixation durations during normal reading correlate with processing difficulty but the specific cognitive mechanisms reflected in these measures are not well understood. This study finds support in German readers’ eyefixations for two distinct difficulty metrics: surprisal, which reflects the change in probabilities across syntactic analyses as new words are integrated, and retrieval, which quantifies comprehension difficulty in terms of working memory constraints. We examine the predictions of both metrics using a family of dependency parsers indexed by an upper limit on the number of candidate syntactic analyses they retain at successive words. Surprisal models all fixation measures and regression probability. By contrast, retrieval does not model any measure in serial processing. As more candidate analyses are considered in parallel at each word, retrieval can account for the same measures as surprisal. This pattern suggests an important role for ranked parallelism in theories of sentence comprehension.
Parsing costs as predictors of reading difficulty: An evaluation using the Potsdam Sentence Corpus
(2008)
The surprisal of a word on a probabilistic grammar constitutes a promising complexity metric for human sentence comprehension difficulty. Using two different grammar types, surprisal is shown to have an effect on fixation durations and regression probabilities in a sample of German readers’ eye movements, the Potsdam Sentence Corpus. A linear mixed-effects model was used to quantify the effect of surprisal while taking into account unigram and bigram frequency, word length, and empirically-derived word predictability; the so-called “early” and “late” measures of processing difficulty both showed an effect of surprisal. Surprisal is also shown to have a small but statistically non-significant effect on empirically-derived predictability itself. This work thus demonstrates the importance of including parsing costs as a predictor of comprehension difficulty in models of reading, and suggests that a simple identification of syntactic parsing costs with early measures and late measures with durations of post-syntactic events may be difficult to uphold.
The boundary paradigm (Rayner, 1975) with a novel preview manipulation was used to examine the extent of parafoveal processing of words to the right of fixation. Words n+1 and n+2 had either correct or incorrect previews prior to fixation (prior to crossing the boundary location). In addition, the manipulation utilized either a high or low frequency word in word n+1 location on the assumption that it would be more likely that n+2 preview effects could be obtained when word n+1 was high frequency. The primary findings were that there was no evidence for a preview benefit for word n+2 and no evidence for parafoveal-on-foveal effects when word n+1 is at least four letters long. We discuss implications for models of eye-movement control in reading.
Parafoveal Load of Word N+1 Modulates Preprocessing Effectivenessof Word N+2 in Chinese Reading
(2010)
Preview benefits (PBs) from two words to the right of the fixated one (i.e., word N+2)and associated parafoveal-on-foveal effects are critical for proposals of distributed lexical processing during reading. This experiment examined parafoveal processing during reading of Chinese sentences, using a boundary manipulation of N+2-word preview with low- and high-frequency words N+1. The main findings were (a) an identity PB for word N+2 that was (b) primarily observed when word N+1 was of high frequency (i.e., an interaction between frequency of word N+1 and PB for word N+2), and (c) a parafoveal-on-foveal frequency effect of word N+1 for fixation durations on word N. We discuss implications for theories of serial attention shifts and parallel distributed processing of words during reading.
We examined individual differences in masked repetition priming by re-analyzing item-level response-time (RT) data from three experiments. Using a linear mixed model (LMM) with subjects and items specified as crossed random factors, the originally reported priming and word-frequency effects were recovered. In the same LMM, we estimated parameters describing the distributions of these effects across subjects. Subjects’ frequency and priming effects correlated positively with each other and negatively with mean RT. These correlation estimates, however, emerged only with a reciprocal transformation of RT (i.e., -1/RT), justified on the basis of distributional analyses. Different correlations, some with opposite sign, were obtained (1) for untransformed or logarithmic RTs or (2) when correlations were computed using within-subject analyses. We discuss the relevance of the new results for accounts of masked priming, implications of applying RT transformations, and the use of LMMs as a tool for the joint analysis of experimental effects and associated individual differences.
There has been a substantial increase in the percentage for publications with co-authors located in departments from different countries in 12 major journals of psychology. The results are evidence for a remarkable internationalization of psychological research, starting in the mid 1970s and increasing in rate at the beginning of the 1990s. This growth occurs against a constant number of articles with authors from the same country; it is not due to a concomitant increase in the number of co-authors per article. Thus, international collaboration in psychology is obviously on the rise.
Microsaccades are very small, involuntary flicks in eye position that occur on average once or twice per second during attempted visual fixation. Microsaccades give rise to EMG eye muscle spikes that can distort the spectrum of the scalp EEG and mimic increases in gamma band power. Here we demonstrate that microsaccades are also accompanied by genuine and sizeable cortical activity, manifested in the EEG. In three experiments, high-resolution eye movements were corecorded with the EEG: during sustained fixation of checkerboard and face stimuli and in a standard visual oddball task that required the counting of target stimuli. Results show that microsaccades as small as 0.15° generate a field potential over occipital cortex and midcentral scalp sites 100 –140 ms after movement onset, which resembles the visual lambda response evoked by larger voluntary saccades. This challenges the standard assumption of human brain imaging studies that saccade-related brain activity is precluded by fixation, even when fully complied with. Instead, additional cortical potentials from microsaccades were present in 86% of the oddball task trials and of similar amplitude as the visual response to stimulus onset. Furthermore, microsaccade probability varied systematically according to the proportion of target stimuli in the oddball task, causing modulations of late stimulus-locked event-related potential (ERP) components. Microsaccades present an unrecognized source of visual brain signal that is of interest for vision research and may have influenced the data of many ERP and neuroimaging studies.