On the linear complexity of Sidel'nikov Sequences over Fd

We study the linear complexity of sequences over the prime field Fd introduced by Sidel’nikov. For several classes of period length we can show that these sequences have a large linear complexity. For the ternary case we present exact results on the linear complexity using well known results on cyclotomic numbers. Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences. The obtained results extend known results on the binary case. Finally we present an upper bound on the aperiodic autocorrelation

Approximation of the discrete logarithm in finite fields of even characteristic by real polynomials

summary:We obtain lower bounds on degree and additive complexity of real polynomials approximating the discrete logarithm in finite fields of even characteristic. These bounds complement earlier results for finite fields of odd characteristic

On the linear complexity of Sidel'nikov sequences over nonprime fields

We introduce a generalization of Sidel'nikov sequences for arbitrary finite fields. We show that several classes of Sidel'nikov sequences over arbitrary finite fields exhibit a large linear complexity. For Sidel'nikov sequences over F-8 we provide exact values for their linear complexity

Approximation of the discrete logarithm in finite fields of even characteristic by real polynomials

summary:We obtain lower bounds on degree and additive complexity of real polynomials approximating the discrete logarithm in finite fields of even characteristic. These bounds complement earlier results for finite fields of odd characteristic

Simiate and the focal adhesion kinase FAK1 cooperate in the regulation of dendritogenesis

Despite the crucial importance of dendritogenesis for the correct functioning of neurons, the molecular mechanisms underlying neuronal arborisation are still not well understood. Current models suggest that distinct parts and phases of dendritic development are regulated by the expression of distinct transcription factors, that are able to target the cytoskeleton. Two proteins recently implicated in dendritogenesis are the Focal Adhesion Kinase FAK1 and the Actin-binding protein Simiate. Using heterologous expression systems as well as mouse brain extracts in combination with coprecipitation assays, we show that Simiate is able to associate with FAK1. Differential centrifugation experiments further revealed the interaction to be present in cytosolic as well as nuclear fractions. Inside the nucleus though, Simiate preferentially binds to a FAK1 isoform of 80 kDa, which has previously been shown to regulate transcription factor activity. Investigating the function of both proteins in primary hippocampal cultures, we further found that FAK1 and Simiate have distinct roles in dendritogenesis: While FAK1 increases dendrite length and number, Simiate preferentially enhances growth and branching. However, if being confined to the nucleus, Simiate selectively triggers primary dendrite formation, enhancing transcription activity at the same time. Since the effect on primary dendrites is specifically re-normalized by a co-expression of FAK1 and Simiate in the nucleus, the data implies that the two proteins interact to counterbalance each other in order to control dendrite formation. Looking at the role of the cytosolic interaction of FAK1 and Simiate, we found that neurotrophin induced dendritogenesis causes a striking colocalisation of FAK1 and Simiate in dendritic growth cones, which is not present otherwise, thus suggesting that the cytosolic interaction stimulates growth cone mediated dendritogenesis in response to certain external signals. Taken together, the data show that FAK1 and Simiate exert several and distinct actions during the different phases of dendritogenesis and that these actions are related to their subcellular localisation and their interaction

Measuring Implicit Motives with the Picture Story Exercise (PSE): Databases of Expert-Coded German Stories, Pictures, and Updated Picture Norms

We present two openly accessible databases related to the assessment of implicit motives using Picture Story Exercises (PSEs): (a) A database of 183,415 German sentences, nested in 26,389 stories provided by 4,570 participants, which have been coded by experts using Winter's coding system for the implicit affiliation/intimacy, achievement, and power motives, and (b) a database of 54 classic and new pictures which have been used as PSE stimuli. Updated picture norms are provided which can be used to select appropriate pictures for PSE applications. Based on an analysis of the relations between raw motive scores, word count, and sentence count, we give recommendations on how to control motive scores for story length, and validate the recommendation with a meta-analysis on gender differences in the implicit affiliation motive that replicates existing findings. We discuss to what extent the guiding principles of the story length correction can be generalized to other content coding systems for narrative material. Several potential applications of the databases are discussed, including (un)supervised machine learning of text content, psychometrics, and better reproducibility of PSE research

Evolutionary history of the Lake Tanganyika cichlid tribe Lamprologini (Teleostei: Perciformes) derived from mitochondrial and nuclear DNA data

Lake Tanganyika comprises a cichlid species flock with substrate-breeding and mouthbrooding lineages. While sexual selection via mate choice on male mating color is thought to boost speciation rates in mouthbrooding cichlids, this is not the case in substrate-breeding lamprologines, which mostly form stable pairs and lack sexual dichromatism. We present a comprehensive reconstruction of the evolution of the cichlid tribe Lamprologini, based upon mtDNA sequences and multilocus nuclear DNA (AFLP) markers. Twelve mtDNA clades were identified, seven of which were corroborated by the AFLP tree. The radiation is likely to have started about 5.3 MYA, contemporarily with that of the mouthbrooding C-lineage, and probably triggered by the onset of deep-water conditions in Lake Tanganyika. Neither the Congo- nor the Malagarazi River species form the most ancestral branch. Several conflicts in the mtDNA phylogeny with taxonomic assignments based upon color, eco-morphology and behavior could be resolved and complemented by the AFLP analysis. Introgressive hybridization upon secondary contact seems to be the most likely cause for paraphyly of taxa due to mtDNA capture in species involving brood-care helpers, while accidental hybridization best explains the para- or polyphyly of several gastropod shell breeders. Taxonomic error or paraphyly due to the survival of ancestral lineages appear responsible for inconsistencies in the genera Lamprologus and Neolamprologus