Time-dependent ARMA modeling of genomic sequences

<p>Abstract</p> <p>Background</p> <p>Over the past decade, many investigators have used sophisticated time series tools for the analysis of genomic sequences. Specifically, the correlation of the nucleotide chain has been studied by examining the properties of the power spectrum. The main limitation of the power spectrum is that it is restricted to stationary time series. However, it has been observed over the past decade that genomic sequences exhibit non-stationary statistical behavior. Standard statistical tests have been used to verify that the genomic sequences are indeed not stationary. More recent analysis of genomic data has relied on time-varying power spectral methods to capture the statistical characteristics of genomic sequences. Techniques such as the evolutionary spectrum and evolutionary periodogram have been successful in extracting the time-varying correlation structure. The main difficulty in using time-varying spectral methods is that they are extremely unstable. Large deviations in the correlation structure results from very minor perturbations in the genomic data and experimental procedure. A fundamental new approach is needed in order to provide a stable platform for the non-stationary statistical analysis of genomic sequences.</p> <p>Results</p> <p>In this paper, we propose to model non-stationary genomic sequences by a time-dependent autoregressive moving average (TD-ARMA) process. The model is based on a classical ARMA process whose coefficients are allowed to vary with time. A series expansion of the time-varying coefficients is used to form a generalized Yule-Walker-type system of equations. A recursive least-squares algorithm is subsequently used to estimate the time-dependent coefficients of the model. The non-stationary parameters estimated are used as a basis for statistical inference and biophysical interpretation of genomic data. In particular, we rely on the TD-ARMA model of genomic sequences to investigate the statistical properties and differentiate between coding and non-coding regions in the nucleotide chain. Specifically, we define a quantitative measure of randomness to assess how far a process deviates from white noise. Our simulation results on various gene sequences show that both the coding and non-coding regions are non-random. However, coding sequences are "whiter" than non-coding sequences as attested by a higher index of randomness.</p> <p>Conclusion</p> <p>We demonstrate that the proposed TD-ARMA model can be used to provide a stable time series tool for the analysis of non-stationary genomic sequences. The estimated time-varying coefficients are used to define an index of randomness, in order to assess the statistical correlations in coding and non-coding DNA sequences. It turns out that the statistical differences between coding and non-coding sequences are more subtle than previously thought using stationary analysis tools: Both coding and non-coding sequences exhibit statistical correlations, with the coding regions being "whiter" than the non-coding regions. These results corroborate the evolutionary periodogram analysis of genomic sequences and revoke the stationary analysis' conclusion that coding DNA behaves like random sequences.</p

Synchronic, optical transmission data link integrated with FPGA circuits

The X-ray free-electron laser X-FEL that is being planned at the DESY research center in cooperation with European partners will produce high-intensity ultra-short X-ray flashes with the properties of laser light. This new light source, which can only be described in terms of superlatives, will open up a whole range of new possibilities for the natural sciences. It could also offer very promising opportunities for industrial users.SIMCON (SIMulator and CONtroller) is the project of the fast, low latency digital controller dedicated to the LLRF$^1$ system in VUV FEL experiment It is being developed by the ELHEP$^2$ group in the Institute of Electronic Systems at Warsaw University of Technology. The main purpose of the project is to create a controller to stabilize the vector sum of fields in cavities of one cryo-module in the experiment. The device can be also used as the simulator of the cavity and test bench for other devices.The synchronic, optical link project was made for the accelerator X-FEL laser TESLA, the LLRF control system experiment at DESY, Hamburg. The control and diagnostic data is transmitted up to 2.5Gbit/s through a plastic fiber in a distance up to a few hundred meters. The link is synchronized once after power up, and never resynchronized when data is transmitted with maximum speed. The one way link bit error rate is less then 10$^{-15}$. The transceiver component written in VHDL that works in the dedicated Altera® Stratix® GX FPGA circuit. During the work in the PERG laboratory a 2,5Gbit/s serial link with the long vector parallel interface transceiver was created. Long-Data-Vector transceiver transmits 16bit vector each 8ns with 120ns latency

FPGA Based, Full-Duplex, Multi-Channel, Multi-Gigabit, Optical, Synchronous Data Transceiver for TESLA Technology LLRF Control System

It may be predicted now, even assuming very conservative approach, that the next generation of the Low Level RF control systems for future accelerators will use extensively such technologies like: very fast programmable circuits equipped with DSP, embedded PC and optical communication I/O functionalities, as well as multi-gigabit optical transmission ofmeasurement data and control signals. The paper presents the idea and realization of a gigabit synchronous data distributor designed to work in the LLRF control system of TESLA technology based X-ray FEL. Thedesign bases on a relatively simple and cheap FPGA chip Cyclone. Commercially availableSERDES (serializer/deserializer) and optical transceiver chips were applied. The optoelectronic module is embedded on the main LLRF BMB (backbone mother board). The MB provides communication with the outside computer control system, programmable chip configuration, integration with other functional modules and power supply. The hardware implementation is here described and the used software for BER (bit-error-rate) testing of themulti-gigabit optical link. The measurement results are presented. The appendix contains acomparison between the available protocols of serial data transmission for FPGA technology. This TESLA Technology Report is a partial contribution to the next version of the SIMCON system which is expected to be released this year. The SIMCON, ver 3. will contain 8 channels and multi-gigabit optical transmission capability

FPGA and optical network based LLRF distributed control system for TESLA-XFEL Linear Accelerator

The work presents a structural and functional model of a distributed low level radio frequency (LLRF) control system for the TESLA-XFEL accelerator. The design of a system basing on the FPGA chips and multi-gigabit optical network was debated. The system design approach was fully parametric. The major emphasis is put on the methods of the functional and hardware concentration to use fully both: a very big transmission capacity of the optical fiber telemetric channels and very big processing power of the latest series of the, DSP enhanced and optical I/O equipped, FPGA chips. The subject of the work is the design of a universal, laboratory module of the LLRF sub-system. Initial parameters of the system model under the design are presented

TESLA Report 2004-09 FPGA and optical network based LLRF distributed control system for TESLA-XFEL Linear Accelerator

The work presents a structural and functional model of a distributed low level radio frequency (LLRF) control system for the TESLA-XFEL accelerator. The design of a system basing on the FPGA chips and multi-gigabit optical network was debated. The system design approach was fully parametric. The major emphasis is put on the methods of the functional and hardware concentration to use fully both: a very big transmission capacity of the optical fiber telemetric channels and very big processing power of the latest series of the, DSP enhanced and optical I/O equipped, FPGA chips. The subject of the work is the design of a universal, laboratory module of the LLRF sub-system. Initial parameters of the system model under the design are presented Keywords: Super conducting cavity control, signal conversion, FPGA, DSP, optics fibers, FPGA with optical I/O, free electron laser, FE