A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic Cost

We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms that improve the convergence performance of the conventional algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and extends the stability bound on the step size. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyzes and simulation results. We show the extended stability bound of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.Comment: Submitted to IEEE Transactions on Signal Processin

Stochastic Subgradient Algorithms for Strongly Convex Optimization over Distributed Networks

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a different node, and a limited number of gradient oracle calls is allowed at each node. In this framework, we introduce a convex optimization algorithm based on the stochastic gradient descent (SGD) updates. Particularly, we use a carefully designed time-dependent weighted averaging of the SGD iterates, which yields a convergence rate of $O\left(\frac{N\sqrt{N}}{T}\right)$ after $T$ gradient updates for each node on a network of $N$ nodes. We then show that after $T$ gradient oracle calls, the average SGD iterate achieves a mean square deviation (MSD) of $O\left(\frac{\sqrt{N}}{T}\right)$. This rate of convergence is optimal as it matches the performance lower bound up to constant terms. Similar to the SGD algorithm, the computational complexity of the proposed algorithm also scales linearly with the dimensionality of the data. Furthermore, the communication load of the proposed method is the same as the communication load of the SGD algorithm. Thus, the proposed algorithm is highly efficient in terms of complexity and communication load. We illustrate the merits of the algorithm with respect to the state-of-art methods over benchmark real life data sets and widely studied network topologies

Optimization of Water Treatment Parameters using Processed Moringa oleifera As a Natural Coagulant for Low Turbidity Water

Moringa oleifera is a natural coagulant which can be used for water treatment in tropical developing countries. This study presents the results of production of natural coagulant from processed Moringa oleifera with simple technique (oil extraction, salt extraction, and microfiltration with 0.2 μm). The optimization study on physical factors was carried out for coagulation-flocculation process. Low initial turbidity water samples (synthetic and river water) were used with turbidity less than 50 Nephelometric Turbidity Units (NTU). The response surface methodology (RSM) was used, and the analysis of variance (ANOVA) was performed to validate the developed regression model. The residual turbidity obtained was 4.514 NTU for synthetic water and 1.598 NTU for river water by applying the optimum conditions of 40 rpm (low speed), mixing time of 41 minutes, and Moringa oleifera dosage of 0.75 mg/L

Introducing a Manipulated System of Drainage Basins of a Developing Countries

As a natural open system, in a drainage basin, there is water flow and balanced channel characteristics. In a manipulated channel system, however, according to Mrowka (1974) and Schumm (1977), the water flow is made under control that induces dynamics in channel characteristics. In this paper, attempt is made to uncover how channel project is caused, nature of the new forms of channel cross-sectional area, shape, sinuosity, and gradient, as well as flood-plain characteristics. It also covers the peculiar transformation evolved as drainage basin system is changed to channel project. Consequently in the paper, two tasks involved were explained. These are significant channel re-construction, and redirection of stream flow as relates to developing water terrace in the savanna zone of Nigeria with the increased channel project dated back 1970s (Olofin, 1980). Specifically, the paper drew considered the physical characteristics of the natural channel of River Suka in North Central Nigeria and the manipulated system or the new face of the drainage basin project of the Kano River, Nigeria used to structure the Tiga dam that involved downstream channel adjustments Keywords: drainage basin, channel, river, dam, downstrea

Moringa oleifera seeds as natural coagulant for water treatment

Developing countries and third world countries are facing potable water supply problems because of inadequate financial resources. The cost of water treatment is increasing and the quality of river water is not stable due to suspended and colloidal particle load caused by land development and high storm runoff during the rainy seasons especially in a country like Malaysia. During the rainy seasons the turbidity level increases and the need for water treatment chemicals increase as well, which leads to high cost of treatment which the water treatment cannot sustain. As a result, the drinking water that reaches the consumer is not properly treated. Therefore, it is of great importance to find a natural alternative for water coagulant to treat the turbidity. It has been found that Moringa oleifera is the best natural coagulant discovered yet, that can replace aluminium sulphate (Alum) which is used widely all around the world. The study is focusing in Moringa oleifera seeds to find the active constituents which are responsible about the coagulation mechanism and improving the coagulation property. This will help in producing this alternative locally as Moringa oleifera is grown in Malaysia and other tropical countries and can be of great benefit for water treatment