This paper describes an artificial neuron structure and an efficient learning procedure in the complex domain. This artificial neuron aims at incorporating an improved aggregation operation on the complex-valued signals. The aggregation operation is based on the idea underlying the weighted root-power mean of input signals. This aggregation operation allows modeling the degree of compensation in a natural manner and includes various aggregation operations as its special cases. The complex resilient propagation algorithm ([Formula: see text]-RPROP) with error-dependent weight backtracking step accelerates the training speed significantly and provides better approximation accuracy. Finally, performance evaluation of the proposed complex root-power mean neuron with the [Formula: see text]-RPROP learning algorithm on various typical examples is given to understand the motivation.

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Notch signaling is an evolutionary conserved process that influences cell fate determination, cell proliferation, and cell death in a context-dependent manner. Notch signaling is fine-tuned at multiple levels and misregulation of Notch has been implicated in a variety of human diseases. We have characterized maheshvara (mahe), a novel gene in Drosophila melanogaster that encodes a putative DEAD box protein that is highly conserved across taxa and belongs to the largest group of RNA helicase. A dynamic pattern of mahe expression along with the maternal accumulation of its transcripts is seen during early stages of embryogenesis. In addition, a strong expression is also seen in the developing nervous system. Ectopic expression of mahe in a wide range of tissues during development results in a variety of defects, many of which resemble a typical Notch loss-of-function phenotype. We illustrate that ectopic expression of mahe in the wing imaginal discs leads to loss of Notch targets, Cut and Wingless. Interestingly, Notch protein levels are also lowered, whereas no obvious change is seen in the levels of Notch transcripts. In addition, mahe overexpression can significantly rescue ectopic Notch-mediated proliferation of eye tissue. Further, we illustrate that mahe genetically interacts with Notch and its cytoplasmic regulator deltex in trans-heterozygous combination. Coexpression of Deltex and Mahe at the dorso-ventral boundary results in a wing-nicking phenotype and a more pronounced loss of Notch target Cut. Taken together we report identification of a novel evolutionary conserved RNA helicase mahe, which plays a vital role in regulation of Notch signaling. KEYWORDS Drosophila; DEAD box helicase; Notch signaling; RNA-binding protein; RNA helicase N OTCH signaling is an evolutionary conserved process that mediates cell-cell communication, which ultimately regulates cell fate (Artavanis-Tsakonas et al. 1999). Notch signaling is critical for many developmental processes and aberrant notch signaling has been related to many human diseases including cancer (Gridley 2003). Notch encodes a trans-membrane receptor that comprises an extracellular domain (NECD) and an intracellular domain (NICD). Notch is expressed at the cell surface as a heterodimeric receptor that is a result of furin-dependent cleavage (S1) occurring in the trans-Golgi network. At the cell surface it physically interacts with the ligands that are expressed in the apposing cells. This interaction with the ligand facilitates a series of proteolytic cleavages, ultimately resulting in the release of NICD. Released NICD translocates into the nucleus, where it interacts with a DNA binding protein CSL (mammalian CBF1/Drosophila Suppressor of Hairless/C. elegans Lag-1) and activates downstream gene expression, by relieving the repressor complex that silences Notch target genes (ArtavanisTsakonas et al. 1983;Logeat et al. 1998;Struhl and Greenwald 1999;Brou et al. 2000;Kopan 2002;Lieber et al. 2002). Finetuning of Notch signaling is mediated by a vast num...

The computational power of a neuron lies in the spatial grouping of synapses belonging to any dendrite tree. Attempts to give a mathematical representation to the grouping process of synapses continue to be a fascinating field of work for researchers in the neural network community. In the literature, we generally find neuron models that comprise of summation, radial basis or product aggregation function, as basic unit of feed-forward multilayer neural network. All these models and their corresponding networks have their own merits and demerits. The MLP constructs global approximation to input-output mapping, while a RBF network, using exponentially decaying localized non-linearity, constructs local approximation to input-output mapping. In this paper, we propose two compensatory type novel aggregation functions for artificial neurons. They produce net potential as linear or non-linear composition of basic summation and radial basis operations over a set of input signals. The neuron models based on these aggregation functions ensure faster convergence, better training and prediction accuracy. The learning and generalization capabilities of these neurons have been tested over various classification and functional mapping problems. These neurons have also shown excellent generalization ability over the two-dimensional transformations.

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The nonlinear spatial grouping process of synapses is one of the fascinating methodologies for neuro-computing researchers to achieve the computational power of a neuron. Generally, researchers use neuron models that are based on summation (linear), product (linear) or radial basis (nonlinear) aggregation for the processing of synapses, to construct multi-layered feed-forward neural networks, but all these neuron models and their corresponding neural networks have their advantages or disadvantages. The multi-layered network generally uses for accomplishing the global approximation of input–output mapping but sometimes getting stuck into local minima, while the nonlinear radial basis function (RBF) network is based on exponentially decaying that uses for local approximation to input–output mapping. Their advantages and disadvantages motivated to design two new artificial neuron models based on compensatory aggregation functions in the quaternionic domain. The net internal potentials of these neuron models are developed with the compositions of basic summation (linear) and radial basis (nonlinear) operations on quaternionic-valued input signals. The neuron models based on these aggregation functions ensure faster convergence, better training, and prediction accuracy. The learning and generalization capabilities of these neurons are verified through various three-dimensional transformations and time series predictions as benchmark problems. Highlights Two new CSU and CPU neuron models for quaternionic signals are proposed. Net potentials based on the compositions of summation and radial basis functions. The nonlinear grouping of synapses achieve the computational power of proposed neurons. The neuron models ensure faster convergence, better training and prediction accuracy. The learning and generalization capabilities of CSU/CPU are verified by various benchmark problems.

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