Ahmad Rushdi

A DSP Approach for Finding the Codon Bias in DNA Sequences

The detection of different forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have primarily focussed on assigning numerical values to the symbolic DNA sequence and then applying spectral analysis tools such as the short-time discrete Fourier transform (ST-DFT) to locate these repeats. A key application of DNA periodicity finding has been in the identification of the protein coding regions in DNA sequences by tracking the so-called period-3 component using the DNA spectrum. The main problem with this gene detection approach is that it is successful for certain genes but does not work for others. An interesting open research problem is to therefore determine the underlying reasons behind this disparity in performance. This requires, in turn, a solid understanding of the working principles of the period-3 component and the DNA spectrum. In this paper, we present a DSP-based approach that provides a complete analysis of this phenomenon. Specifically, we derive a new DSP based model that 1) clearly explains the underlying mechanism of the period-3 component, 2) directly relates the identification of the period-3 component to the detection of nucleotide bias in the codon structure, and 3) completely characterizes the DNA spectrum by a set of numerical sequences termed the filtered polyphase sequences. Furthermore, by adhering to the specific structure of the derived model, we can show that standard signal processing tools such as digital filtering can substantially enhance the detection of the codon bias. Several performance measures of DNA periodicity detection are also proposed and experimental results are provided to illustrate the key findings of our work.

Gene Identification Using the Z-Curve Representation

DSP based techniques have been recently proposed to identify the protein coding regions in a DNA strand by detecting the so-called period-3 component in the DNA spectrum. The DNA spectrum is computed after mapping the DNA symbolic sequence to numerical digital sequences. A typical choice of mapping is the Voss representation. In this paper, we propose the use of a more elaborate mapping scheme, namely the Z-curve representation. Using a multirate signal processing approach, we derive closed form expressions to compute the Z-curve based DNA spectrum as well as mathematical conditions that characterize the coding regions. The derived formulas also prove that the Z-curve representation yields essentially the same DNA spectrum as the one obtained using the Voss representation at a lower computational cost

PAPR Reduction in Trigonometric-Based OFDM Systems

A key building block in any OFDM transceiver is the Fast Fourier Transform (FFT) and its inverse. A number of researchers have recently proposed the use of the discrete cosine transform (DCT) and the discrete sine transform (DST), and their inverses as alternative modulating/demodulating bases to improve the BER performance of OFDM schemes while maintaining a low implementation cost. In this paper, we consider the open problem of reducing the peak-to-average power ratio (PAPR) in OFDM systems that deploy these trigonometric transforms. In specific, we show that similar to the FFT case, the complex envelope of a bandlimited DCT/DST- OFDM signal has a chi-square distribution with one degree of freedom and hence converges weakly to a Gaussian random process as the number of sub-carriers becomes large. Using this result, we then derive closed form expressions for the complementary cumulative distribution functions (CCDF) of each system and show that OFDM systems with trigonometric transforms provide higher PAPR reduction than the standard FFT-based system. Simulation results that compare the CCDFs of the different transforms using the partial transmit sequences (PTS) technique confirm our theoretical findings.

A DSP perspective to the period-3 detection problem

Many signal processing techniques have been introduced in the past to identify the protein coding regions by detecting the so-called period-3 component in the DNA spectrum. However, a solid understanding of this observed phenomenon and its underlying mechanism from a DSP perspective has been missing from the literature. We therefore propose a novel DSP model that i) clearly explains the intricate operation of the DNA spectrum, ii) allows the derivation of new DNA spectrum expressions which, in turn, generalize and unify previous work and iii) suggests an efficient way to improve the detection of protein coding regions by computing a filtered spectrum.

The role of the symbolic-to-numerical mapping in the detection of DNA periodicities

The detection of many forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have used the simple Voss mapping to map the symbolic DNA sequence into binary indicator ones before computing some form of the so-called DNA spectrum to locate these repeats. A key research issue that remains however open is whether the success of these techniques is Voss specific. In this paper, we first propose a new and generic matrix based framework that comprises most of the widely used mappings in the literature as special cases. By using this approach, we can then show that the standard DNA spectrum is in fact in variable under most of these mappings. Finally, we demonstrate that a number of potential new mappings naturally follow from the suggested framework.

Trigonometric transforms for finding repeats in DNA sequences

The detection of many forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have primarily focussed on using the short-time discrete Fourier transform (ST-DFT) as the key tool in identifying such repeat sequences. In this paper, we propose to use different fast discrete transforms such as the discrete cosine transform (DCT), the discrete sine transform (DST), and the discrete Hartley transform (DHT), to locate these patterns. In specific, we derive a new unified multirate DSP model that i) allows the derivation of new closed form DNA spectrum expressions for the above trigonometric transforms, ii) includes the DFT model as a special case, and iii) suggests an efficient way to improve the detection of repeats by digital filtering.

The Filtered Spectral Rotation Measure

Many signal processing techniques were proposed in the past to identify the so-called period-3 component in the protein coding regions of DNA sequences. Most of these methods evaluate the magnitude of the output of an M-point sliding window DFT at the frequency k = M/3. In this paper, we introduce a new multirate DSP approach that computes the phase of the output of the sliding window DFT at the above frequency. We first show that, similar to the magnitude case, the phase component is completely denned by the so-called filtered polyphase sequences. We then propose the filtered spectral rotation measure for detecting the periodicity in genetic regions by modifying the polyphase sequences using digital filters. Experimental results show that the new filtered measure performs better than the existing non-filtered approaches.

Disk density tuning of a maximal random packing

We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson‐disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more‐aggressive local operations. We may achieve a user‐defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict‐free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially‐varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non‐obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.

A New DSP-Based Measure for CPG Islands Detection

Identification of DNA regions that are rich in the CpG pattern is important because such segments are resistant to methylation and are typically associated with genes that are frequently switched on. In this paper, we propose a DSP based approach to detect such regions. In specific, we first derive two new Markov chain models for CpG and non-CpG regions respectively and then design a number of FIR filters to generate a filtered Likelihood Ratio Test (LRT) measure. Our simulations show that the joint design of the probabilistic models and the digital filter produces significantly better results than previous work

All-quad meshing without cleanup

We present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometryquadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.