Two-band fast Hartley transform

This article has been made available through the Brunel Open Access Publishing Fund.Efficient algorithms have been developed over the past 30 years for computing the forward and inverse discrete Hartley transforms (DHTs). These are similar to the fast Fourier transform (FFT) algorithms for computing the discrete Fourier transform (DFT). Most of these methods seek to minimise the complexity of computations and or the number of operations. A new approach for the computation of the radix-2 fast Hartley transform (FHT) is presented. The proposed algorithm, based on a two-band decomposition of the input data, possesses a very regular structure, avoids the input or out data shuffling, requires slightly less multiplications than the existing approaches, but increases the number of additions

Molecular Analysis of a Major Carpel Developmental Regulator: CRABS CLAW’s Protein Domains and Non-Cell-Autonomous Action

CRABS CLAW is a small protein belonging to the YABBY family, a plant specific protein family. In Arabidopsis thaliana it is expressed in the developing carpels and regulates the apical fusion of the two carpels, transmitting tract development, lateral growth, and nectary formation. The expression of CRC is rather complex with multiple expression domains throughout the young gynoecium and as for other YABBY proteins a non-cell-autonomous action has been described. However, only few regulators of CRC expression and target genes are described and the mode of non-cell-autonomous action is still unknown. This dissertation aims to identify transcriptional regulators, responsible for the proper temporal and spatial expression of CRC, the specification of CRC’s place in the adaxial-abaxial regulatory network and to clarify the means of its non-cell-autonomous action. The regulation of CRC expression has been analyzed via a large scale Yeast-1-Hybrid screen and identified over 100 potential regulators of CRC expression, integrating CRC tightly into the carpel developmental regulatory protein network. Further analysis of CRC function through expression analysis led to the identification of target genes of CRC like mir165/166, members of the KANADI gene family, and the HD ZIP III gene family. Both gene families are major players in the adaxial-abaxial regulatory network, involved in the development of all lateral plant organs such as leaves and floral organs. CRC supports KANADI action and activates the expression of other involved factors. In addition, CRC directly targets members of the HD ZIP III family. However, CRC’s position in the adaxial- abaxial regulatory network seems to be not conserved in other eudicots. CRC exhibits a non- cell-autonomous action which is conferred by at least two signaling pathways. Abaxial polarity is regulated by the activation of the mobile miRNA165/166. At the same time, localizations of GFP tagged CRC revealed the CRC protein to be mobile as it migrates into the adaxial domain in young gynoecia. In older gynoecia it was excluded from the adaxial domain. This study identified multiple unique features of CRC compared to its relatives. Its thightly controlled expression by over 100 putative regulators, integration in complex co-expression networks, adaxial and abaxial target genes, and its two mode non-cell-autonomous action indicate the important role in the complicated carpel development.CRABS CLAW ist ein kleines Protein der pflanzenspezifischen YABBY Protein Familie. In Arabidopsis thaliana ist es in den entwickelnden Fruchtblättern exprimiert und reguliert die apikale Fusion der Fruchtblätter, die Entwicklung des Transmissionskanal (einem Bereich des Septums), die Begrenzung des lateralen Wachstums des Gynoeceums, und die Bildung der Nektarien. Die Expression von CRC ist auf mehrere Bereiche im Fruchtblatt aufgeteilt und ebenso wurde ein nicht-zell-autonomer Effekt wie für andere YABBY Proteine beschrieben. Jedoch sind nur einige wenige Regulatoren der CRC Expression und Zielgene von CRC bekannt, sowie die Natur des mobilen Signals des nicht-zell-autonomen Effektes unbekannt ist. Daher zielt diese Dissertation darauf, zusätzliche transkriptionelle Regulatoren, die für die korrekte zeitliche und räumliche Expression von CRC nötig sind, zu identifizieren, sowie CRCs Position im adaxialen-abaxialen Netzwerk zu identifizieren und die Art und Weise des nicht-zell-autonomen Effektes zu klären. Die Expression von CRC wurde durch eine groß angelegte Hefe-1-Hybrid Analyse näher untersucht und über 100 mögliche Regulatoren der CRC Expression wurden identifiziert. Dies festigt CRCs Position im gen-regulatorischen Netzwerk der Fruchtblattentwicklung. Eine weitere Analyse der CRC Funktionen mittels Expressionsanalyse führte zu der Identifikation mehrerer Zielgene wie mir165/166, Mitglieder der KANADI Genfamilie und Mitglieder der HD ZIP III Genfamilie. Beide Genfamilien sind Hauptkomponenten des adaxial–abaxialen Regulationsnetzwerkes. Dabei unterstützt CRC die Funktion der KAN Proteine und reguliert die Expression anderer involvierter Gene. Zusätzlich reguliert CRC direkt die Expression einiger HD ZIP III Gene. Wobei die Regulation der adaxial-abaxialen Regulatoren durch CRC zwischen verschiedenen Eudikotylen nicht komplett konserviert ist. CRC weist eine nicht-zell-autonome Funktion auf, die durch mindestens zwei Signalübertragungswege vermittelt wird. Zum einen reguliert CRC die abaxiale Polarität durch die Aktivierung der mobilen miRNA165/166 und zum anderen durch direkten Transport des CRC Proteins. Lokalisierungen von mit GFP markierten CRC zeigten, dass das CRC Protein in den frühen Stadien des Gyneoceums von der abaxialen Domäne in die adaxiale wandert. In späteren Stadien ist CRC auf die abaxiale Domäne begrenzt. Diese Studie konnte mehrere einzigartige CRC Charakteristika identifizieren, die CRC von den anderen Mitgliedern der YABBY Familie unterscheidet. Seine stark kontrollierte Expression durch mehr als 100 mögliche Regulatoren, die Integration in ein kompliziertes Co- Expressions Netzwerk, adaxiale und abaxiale Zielgene, und mindestens zwei Möglichkeiten zur nicht-zell-autonomen Regulation, zeigen eindringlich die wichtige Rolle CRCs in der komplexen Karpellentwicklung auf

Polinomno filtriranje: postizanje bilo kojeg stupnja na nepravilno uzorkovanim podacima

Conventionally, polynomial filters are derived for evenly spaced points. Here, a derivation of polynomial filters for irregularly spaced points is provided and illustrated by example. The filter weights and variance reduction factors (VRFs) for both expanding memory polynomial (EMP) and fading-memory polynomial (FMP) filters are programmatically derived so that the expansion up to any degree can be generated. (Matlab was used for doing the symbolic weight derivations utilizing Symbolic Toolbox functions.) Order-switching and length-adaption are briefly considered. Outlier rejection and Cramer-Rao Lower Bound consistency are touched upon. In terms of performance, the VRF and its decay for the EMP filter is derived as a function of length (n) and the switch-over point is calculated where the VRFs of the EMP and FMP filters are equal. Empirical results verifying the derivation and implementation are reported.Polinomni filtri uobičajeno se rade za ravnomjerno raspoređene točke u prostoru. U ovom radu dana je derivacija polinomnih filtara za neravnomjerno raspoređene točke. Težinske vrijednosti filtra i faktori smanjenja varijance (VRF-ovi) za polinom proširene memorije (EMP) i polinom oslabljenje memorije (FMP) su programski podržani tako da se može napraviti ekspanzija do bilo kojeg stupnja. Kratko su razmotreni i promjena poretka i adaptacija dužine filtra. Dotaknute su i metode odbijanja jako raspršenih rezultata i Cramer-Raove konzistencije donje granice. VRF i njegovo opadanje za EMP filtar izvedeno je kao funkcija duljine (n) i izračunata je točka prijelaza gdje su VRF-ovi od EMP i FMP filtara jednaki. Predočeni su empirijski rezultati koji verificiraju izvod i implementaciju