The random projection algorithm detects genetic motifs by:
1) Randomly projecting sequence data onto lower-dimensional subspaces to group similar sequences.
2) Using the grouped sequences to build probabilistic motif models and refine the models through expectation maximization.
3) Iterating the process with multiple random projections and selecting the highest scoring motif model.
The algorithm hashes sequence tuples onto buckets based on random k-tuple projections, builds initial motif models from enriched buckets, and refines the models through local search. It detects motifs through grouping related sequences rather than distance-based methods, handling variations in instances effectively. Parameter selection and multiple iterations increase sensitivity for planted motif detection problems.
1) The document discusses the modulation techniques used in various Global Navigation Satellite Systems (GNSS), including GPS, Glonass, BeiDou, and Galileo.
2) GPS uses BPSK-R modulation with a 2.046 MHz bandwidth. Glonass uses FDMA, while the others use CDMA.
3) BOC modulation, used in Galileo, modulates the signal with a subcarrier signal that can be either sine or cosine. This results in a spectral distribution around the subcarrier frequency.
The document discusses MOSFET circuits and their analysis. It includes:
1) Deriving the I-V characteristics of a MOSFET in triode and saturation regions and using it to calculate values needed for a MOSFET to operate in saturation.
2) Deriving expressions for input resistance, output resistance, voltage gain, and overall gain of a grounded source amplifier and designing a biasing circuit for it.
3) Explaining the operation of a MOSFET current steering circuit with a diagram and calculating the percentage change in drain current when replacing a MOSFET.
How to make hash functions go fast inside snarks, aka a guided tour through arithmetisation friendly hash functions (useful for all cryptographic protocols where cost is dominated by multiplications -- e.g. anything using R1CS; secret sharing based multiparty computation protocols; etc)
I am Frank P. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from Sunway University, Malaysia. I have been helping students with their assignments for the past 8 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems Assignment.
This presentation describes the Fourier Transform used in different mathematical and physical applications.
The presentation is at an Undergraduate in Science (math, physics, engineering) level.
Please send comments and suggestions to improvements to solo.hermelin@gmail.com.
More presentations can be found at my website http://www.solohermelin.com.
I am Arnold H. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, Nanyang Technological University. I have been helping students with their assignments for the past 10 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems Assignment.
This document contains questions pertaining to information theory, coding theory, digital communication, and microprocessors.
For information theory and coding theory, questions assess concepts like entropy, channel capacity, linear block codes, cyclic codes, convolutional codes, and Huffman coding.
For digital communication, questions cover topics such as PCM, sampling, quantization, line coding, optical fiber communication, modulation techniques like BPSK, FSK, and DPSK.
For microprocessors, questions examine memory segmentation, addressing modes, assembler directives, string instructions, interrupts, and 8086 architecture specifics.
1) The document discusses the modulation techniques used in various Global Navigation Satellite Systems (GNSS), including GPS, Glonass, BeiDou, and Galileo.
2) GPS uses BPSK-R modulation with a 2.046 MHz bandwidth. Glonass uses FDMA, while the others use CDMA.
3) BOC modulation, used in Galileo, modulates the signal with a subcarrier signal that can be either sine or cosine. This results in a spectral distribution around the subcarrier frequency.
The document discusses MOSFET circuits and their analysis. It includes:
1) Deriving the I-V characteristics of a MOSFET in triode and saturation regions and using it to calculate values needed for a MOSFET to operate in saturation.
2) Deriving expressions for input resistance, output resistance, voltage gain, and overall gain of a grounded source amplifier and designing a biasing circuit for it.
3) Explaining the operation of a MOSFET current steering circuit with a diagram and calculating the percentage change in drain current when replacing a MOSFET.
How to make hash functions go fast inside snarks, aka a guided tour through arithmetisation friendly hash functions (useful for all cryptographic protocols where cost is dominated by multiplications -- e.g. anything using R1CS; secret sharing based multiparty computation protocols; etc)
I am Frank P. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from Sunway University, Malaysia. I have been helping students with their assignments for the past 8 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems Assignment.
This presentation describes the Fourier Transform used in different mathematical and physical applications.
The presentation is at an Undergraduate in Science (math, physics, engineering) level.
Please send comments and suggestions to improvements to solo.hermelin@gmail.com.
More presentations can be found at my website http://www.solohermelin.com.
I am Arnold H. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, Nanyang Technological University. I have been helping students with their assignments for the past 10 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems Assignment.
This document contains questions pertaining to information theory, coding theory, digital communication, and microprocessors.
For information theory and coding theory, questions assess concepts like entropy, channel capacity, linear block codes, cyclic codes, convolutional codes, and Huffman coding.
For digital communication, questions cover topics such as PCM, sampling, quantization, line coding, optical fiber communication, modulation techniques like BPSK, FSK, and DPSK.
For microprocessors, questions examine memory segmentation, addressing modes, assembler directives, string instructions, interrupts, and 8086 architecture specifics.
This document contains practice problems for a digital signal processing course. It includes 6 sections with multiple parts each:
1) Computing the discrete Fourier transform (DFT) and fast Fourier transform (FFT) of various sequences and plotting the results.
2) Computing the FFT of sequences and plotting the phase and magnitude.
3) Using a decimation in time FFT algorithm to find the DFT of sequences and plotting the results.
4) Questions about sampling an audio signal and computing the DFT and FFT.
5) Determining the circular convolution between two sequences.
6) Computing the circular convolution of two sequences using the DFT, along with related questions.
The document discusses the calculation of magnetic fields generated by electric currents. It begins by defining the Biot-Savart law and provides the formula for calculating the magnetic field generated by a current-carrying wire. It then uses this law to derive integral formulas for the z- and r-components of the magnetic field generated by a long solenoid. It approximates these integrals using a Taylor series expansion to obtain explicit formulas for the magnetic field components as a function of position inside and outside the solenoid. Finally, it presents a graph showing the measured axial magnetic field profile inside a coil carrying a 1A current.
The document is the question paper for the Sixth Semester B.E. Degree Examination in Antennas and Propagation held in December 2013/January 2014. It contains 8 questions divided into 2 parts. Part A contains questions 1-4 covering topics like definitions related to antennas, derivation of expressions for directivity and effective aperture of antennas, field patterns of antenna arrays, and pattern multiplication. Part B contains questions 5-8 related to topics like radiation integrals, antenna arrays, and antenna measurements. Students had to answer 5 questions selecting at least 2 from each part.
In this work, we study H∞ control wind turbine fuzzy model for finite frequency(FF) interval. Less conservative results are obtained by using Finsler’s lemma technique, generalized Kalman Yakubovich Popov (gKYP), linear matrix inequality (LMI) approach and added several separate parameters, these conditions are given in terms of LMI which can be efficiently solved numerically for the problem that such fuzzy systems are admissible with H∞ disturbance attenuation level. The FF H∞ performance approach allows the state feedback command in a specific interval, the simulation example is given to validate our results.
The receiver structure consists of four main components:
1. A matched filter that maximizes the SNR by matching the source impulse and channel.
2. An equalizer that removes intersymbol interference.
3. A timing component that determines the optimal sampling time using an eye diagram.
4. A decision component that determines whether the received bit is a 0 or 1 based on a threshold.
The performance of the receiver depends on factors like noise, equalization technique used, and timing accuracy. The bit error rate can be estimated using tools like error functions.
1. The document discusses numerical integration techniques for approximating definite integrals that cannot be solved analytically. It covers basic techniques like the rectangle, midpoint, and trapezoid rules as well as more accurate techniques like Simpson's rule.
2. Examples are provided to demonstrate calculating definite integrals numerically to approximate values like the natural logarithm of numbers. The document also introduces Monte Carlo integration techniques using random sampling.
3. As an example problem, the document calculates the final speed of a box moving under a time-varying force using numerical integration over the integral expression for work. The Simpson's rule is identified as an approach to implement in a programming code to solve this example.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document discusses three techniques for identifying linear systems: frequency chirp method, inverse filtering method, and coherence function method. The frequency chirp method uses a wideband excitation input like a frequency chirp and obtains the frequency response as the discrete Fourier transform of the system's output. The inverse filtering method uses pseudoinverse to find the impulse response. The coherence function method uses the coherence function and input-output cross-spectrum to estimate the system response directly and inversely. These three techniques were demonstrated on a 10th order Chebyshev filter. The inverse filtering method provided an identification closest to the actual system response compared to the other two techniques.
The document describes an incremental algorithm for computing the Birkhoff resultant polytope Π of a system of n+1 polynomials in n variables. The algorithm takes as input the supports of the polynomials and incrementally constructs an inner approximation Q of Π by calling an oracle to extend illegal facets. At each step Q is refined until all facets are legal, at which point Q = Π. The algorithm outputs the H-representation and V-representation of Π.
This document contains questions related to analog and digital circuits and communication systems. It asks the reader to:
1) Explain different circuit elements and concepts such as capacitors, resistors, MOSFET switches, delay elements, and more.
2) Analyze and design circuits including op-amps, filters, adders, ADCs, and DACs.
3) Discuss digital communication techniques like PCM, differential PPM, PSK, and more.
4) Solve problems involving SNR calculations, quantization noise, error probability, and modulation.
The document contains a summary of a Digital Communication examination paper from December 2012. It includes 20 questions across two parts - Part A and Part B. The questions cover topics like sampling theorem, pulse code modulation, delta modulation, digital modulation techniques, error control coding, spread spectrum techniques and more. Students are required to attempt 5 full questions by selecting at least 2 questions from each part.
This technical note explains how you can very easily use the command line functions available in
the MATLAB signal processing toolbox, to simulate simple multirate DSP systems. The focus
here is to be able to view in the frequency domain what is happening at each stage of a system
involving upsamplers, downsamplers, and lowpass filters. All computations will be performed
using MATLAB and the signal processing toolbox. These same building blocks are available in
Simulink via the DSP blockset. The DSP blockset allows better visualization of the overall system,
but is not available in the ECE general computing laboratory or on most personal systems. A
DSP block set example will be included here just so one can see the possibilities with the additional
MATLAB tools.
The MAIN CONTRIBUTION is an on-line heuristic law to set the training process and to modify the NN topology based on the Levenberg-Marquardt method.
An Area Predictor Filter using nonlinear autoregressive model based on neural networks for time series forecasting is introduced.
The core of the proposal is to analyze the roughness (long or short term stochastic dependence) of time series evaluated by the Hurst parameter (H).
The proposed law adapts in real time the topology of the filter at each stage of time series, changing the number of pattern, the number of iterations and the input vector length.
The main results show a good performance of the predictor, considering in particular to time series whose H parameter has a high roughness of signal, which is evaluated by HS and HA, respectively.
These results encouraged to continue working on new adjustment algorithms for time series modeling natural phenomena.
Pythran: Static compiler for high performance by Mehdi Amini PyData SV 2014PyData
Pythran is a an ahead of time compiler that turns modules written in a large subset of Python into C++ meta-programs that can be compiled into efficient native modules. It targets mainly compute intensive part of the code, hence it comes as no surprise that it focuses on scientific applications that makes extensive use of Numpy. Under the hood, Pythran inter-procedurally analyses the program and performs high level optimizations and parallel code generation. Parallelism can be found implicitly in Python intrinsics or Numpy operations, or explicitly specified by the programmer using OpenMP directives directly in the Python source code. Either way, the input code remains fully compatible with the Python interpreter. While the idea is similar to Parakeet or Numba, the approach differs significantly: the code generation is not performed at runtime but offline. Pythran generates C++11 heavily templated code that makes use of the NT2 meta-programming library and relies on any standard-compliant compiler to generate the binary code. We propose to walk through some examples and benchmarks, exposing the current state of what Pythran provides as well as the limit of the approach.
1) The document discusses various topics in digital communication including sampling, quantization, multiplexing, modulation, and coding.
2) Questions are provided related to topics like Nyquist sampling, TDM, pulse shaping, PCM, and carrier systems.
3) Block diagrams and equations are required to explain concepts like DPCM transmission, matched filtering, and spread spectrum communication.
Brief Introduction About Topological Interference Management (TIM)Pei-Che Chang
This document discusses topological interference management (TIM) techniques for interference channels. TIM exploits interference alignment principles under realistic channel state information assumptions. The key ideas are:
- Focus on canceling strong interference links based on knowledge of the interference pattern
- There is a connection between TIM and the index coding problem
- The goal of TIM is to maximize degrees of freedom (DoF) based on network topology information
- Examples show how transmitting signals over multiple channel uses and exploiting the interference pattern can achieve different DoF values through interference alignment
The document provides information about a digital communication systems exam, including questions on various topics in digital communication such as sampling theory, PCM, delta modulation, baseband transmission, digital modulation techniques, error control coding, and spread spectrum.
The exam is divided into two parts (A and B) and contains 10 questions in total. Part A covers topics such as sampling theorem, signal reconstruction, PCM, delta modulation, baseband transmission, and digital modulation formats. Part B focuses on questions related to digital modulation techniques like BPSK, probability of symbol error, DPSK, and spread spectrum modulation. The document provides detailed questions on concepts, derivations, and design problems in digital communication systems.
1. A giant python swallowed an alligator in Everglades National Park, Florida, according to an article in yesterday's New York Times.
2. The article was titled "Invasion of the Giant Pythons" from PBS Nature.
3. The document provided a brief news item about an incident of a giant python eating an alligator in Florida's Everglades National Park.
This document introduces information theory and channel capacity models. It discusses several channel models including the binary symmetric channel (BSC), binary erasure channel, and additive white Gaussian noise channel. It explains how channel capacity is defined as the maximum rate of error-free transmission and derives the capacity for some basic channels. The document also covers channel coding techniques like interleaving that can improve performance by converting burst errors into random errors.
This document provides an overview of pairwise testing. It begins by defining pairwise testing and explaining that it aims to reduce the number of test cases needed while still covering all pairs of input parameters. It then outlines different methods for generating pairwise test cases, including orthogonal Latin squares, Automatic Efficient Test Generator (AETG), In-Parameter-Order (IPO), and genetic algorithms. The document compares the size of test sets generated by different algorithms and lists several pairwise testing tools. It concludes by mentioning additional references and resources on the topic of pairwise testing.
Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not
obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an
adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering
number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional
feature space using gaussian kernel and clustering in the feature space. The Matlab simulation
results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results
1. The document discusses RNA synthesis and processing, including the different types of RNA (mRNA, rRNA, tRNA), the process of transcription, initiation, elongation, and termination.
2. It also covers RNA processing after transcription, including 5' capping, polyadenylation, splicing, and modifications to tRNA, rRNA and other non-coding RNAs.
3. The clinical applications of understanding RNA synthesis and processing are discussed, such as targets for antibiotics, implications for genetic diseases, and miRNA roles in various human health conditions.
DNA contains genes that code for proteins. During transcription, mRNA is produced by copying DNA in the nucleus. The mRNA then transports the genetic code to the cytoplasm for translation at the ribosome. Translation is the process where tRNA brings amino acids to the ribosome according to the mRNA codons to produce a protein, consisting of a chain of amino acids specified by the DNA.
This document contains practice problems for a digital signal processing course. It includes 6 sections with multiple parts each:
1) Computing the discrete Fourier transform (DFT) and fast Fourier transform (FFT) of various sequences and plotting the results.
2) Computing the FFT of sequences and plotting the phase and magnitude.
3) Using a decimation in time FFT algorithm to find the DFT of sequences and plotting the results.
4) Questions about sampling an audio signal and computing the DFT and FFT.
5) Determining the circular convolution between two sequences.
6) Computing the circular convolution of two sequences using the DFT, along with related questions.
The document discusses the calculation of magnetic fields generated by electric currents. It begins by defining the Biot-Savart law and provides the formula for calculating the magnetic field generated by a current-carrying wire. It then uses this law to derive integral formulas for the z- and r-components of the magnetic field generated by a long solenoid. It approximates these integrals using a Taylor series expansion to obtain explicit formulas for the magnetic field components as a function of position inside and outside the solenoid. Finally, it presents a graph showing the measured axial magnetic field profile inside a coil carrying a 1A current.
The document is the question paper for the Sixth Semester B.E. Degree Examination in Antennas and Propagation held in December 2013/January 2014. It contains 8 questions divided into 2 parts. Part A contains questions 1-4 covering topics like definitions related to antennas, derivation of expressions for directivity and effective aperture of antennas, field patterns of antenna arrays, and pattern multiplication. Part B contains questions 5-8 related to topics like radiation integrals, antenna arrays, and antenna measurements. Students had to answer 5 questions selecting at least 2 from each part.
In this work, we study H∞ control wind turbine fuzzy model for finite frequency(FF) interval. Less conservative results are obtained by using Finsler’s lemma technique, generalized Kalman Yakubovich Popov (gKYP), linear matrix inequality (LMI) approach and added several separate parameters, these conditions are given in terms of LMI which can be efficiently solved numerically for the problem that such fuzzy systems are admissible with H∞ disturbance attenuation level. The FF H∞ performance approach allows the state feedback command in a specific interval, the simulation example is given to validate our results.
The receiver structure consists of four main components:
1. A matched filter that maximizes the SNR by matching the source impulse and channel.
2. An equalizer that removes intersymbol interference.
3. A timing component that determines the optimal sampling time using an eye diagram.
4. A decision component that determines whether the received bit is a 0 or 1 based on a threshold.
The performance of the receiver depends on factors like noise, equalization technique used, and timing accuracy. The bit error rate can be estimated using tools like error functions.
1. The document discusses numerical integration techniques for approximating definite integrals that cannot be solved analytically. It covers basic techniques like the rectangle, midpoint, and trapezoid rules as well as more accurate techniques like Simpson's rule.
2. Examples are provided to demonstrate calculating definite integrals numerically to approximate values like the natural logarithm of numbers. The document also introduces Monte Carlo integration techniques using random sampling.
3. As an example problem, the document calculates the final speed of a box moving under a time-varying force using numerical integration over the integral expression for work. The Simpson's rule is identified as an approach to implement in a programming code to solve this example.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document discusses three techniques for identifying linear systems: frequency chirp method, inverse filtering method, and coherence function method. The frequency chirp method uses a wideband excitation input like a frequency chirp and obtains the frequency response as the discrete Fourier transform of the system's output. The inverse filtering method uses pseudoinverse to find the impulse response. The coherence function method uses the coherence function and input-output cross-spectrum to estimate the system response directly and inversely. These three techniques were demonstrated on a 10th order Chebyshev filter. The inverse filtering method provided an identification closest to the actual system response compared to the other two techniques.
The document describes an incremental algorithm for computing the Birkhoff resultant polytope Π of a system of n+1 polynomials in n variables. The algorithm takes as input the supports of the polynomials and incrementally constructs an inner approximation Q of Π by calling an oracle to extend illegal facets. At each step Q is refined until all facets are legal, at which point Q = Π. The algorithm outputs the H-representation and V-representation of Π.
This document contains questions related to analog and digital circuits and communication systems. It asks the reader to:
1) Explain different circuit elements and concepts such as capacitors, resistors, MOSFET switches, delay elements, and more.
2) Analyze and design circuits including op-amps, filters, adders, ADCs, and DACs.
3) Discuss digital communication techniques like PCM, differential PPM, PSK, and more.
4) Solve problems involving SNR calculations, quantization noise, error probability, and modulation.
The document contains a summary of a Digital Communication examination paper from December 2012. It includes 20 questions across two parts - Part A and Part B. The questions cover topics like sampling theorem, pulse code modulation, delta modulation, digital modulation techniques, error control coding, spread spectrum techniques and more. Students are required to attempt 5 full questions by selecting at least 2 questions from each part.
This technical note explains how you can very easily use the command line functions available in
the MATLAB signal processing toolbox, to simulate simple multirate DSP systems. The focus
here is to be able to view in the frequency domain what is happening at each stage of a system
involving upsamplers, downsamplers, and lowpass filters. All computations will be performed
using MATLAB and the signal processing toolbox. These same building blocks are available in
Simulink via the DSP blockset. The DSP blockset allows better visualization of the overall system,
but is not available in the ECE general computing laboratory or on most personal systems. A
DSP block set example will be included here just so one can see the possibilities with the additional
MATLAB tools.
The MAIN CONTRIBUTION is an on-line heuristic law to set the training process and to modify the NN topology based on the Levenberg-Marquardt method.
An Area Predictor Filter using nonlinear autoregressive model based on neural networks for time series forecasting is introduced.
The core of the proposal is to analyze the roughness (long or short term stochastic dependence) of time series evaluated by the Hurst parameter (H).
The proposed law adapts in real time the topology of the filter at each stage of time series, changing the number of pattern, the number of iterations and the input vector length.
The main results show a good performance of the predictor, considering in particular to time series whose H parameter has a high roughness of signal, which is evaluated by HS and HA, respectively.
These results encouraged to continue working on new adjustment algorithms for time series modeling natural phenomena.
Pythran: Static compiler for high performance by Mehdi Amini PyData SV 2014PyData
Pythran is a an ahead of time compiler that turns modules written in a large subset of Python into C++ meta-programs that can be compiled into efficient native modules. It targets mainly compute intensive part of the code, hence it comes as no surprise that it focuses on scientific applications that makes extensive use of Numpy. Under the hood, Pythran inter-procedurally analyses the program and performs high level optimizations and parallel code generation. Parallelism can be found implicitly in Python intrinsics or Numpy operations, or explicitly specified by the programmer using OpenMP directives directly in the Python source code. Either way, the input code remains fully compatible with the Python interpreter. While the idea is similar to Parakeet or Numba, the approach differs significantly: the code generation is not performed at runtime but offline. Pythran generates C++11 heavily templated code that makes use of the NT2 meta-programming library and relies on any standard-compliant compiler to generate the binary code. We propose to walk through some examples and benchmarks, exposing the current state of what Pythran provides as well as the limit of the approach.
1) The document discusses various topics in digital communication including sampling, quantization, multiplexing, modulation, and coding.
2) Questions are provided related to topics like Nyquist sampling, TDM, pulse shaping, PCM, and carrier systems.
3) Block diagrams and equations are required to explain concepts like DPCM transmission, matched filtering, and spread spectrum communication.
Brief Introduction About Topological Interference Management (TIM)Pei-Che Chang
This document discusses topological interference management (TIM) techniques for interference channels. TIM exploits interference alignment principles under realistic channel state information assumptions. The key ideas are:
- Focus on canceling strong interference links based on knowledge of the interference pattern
- There is a connection between TIM and the index coding problem
- The goal of TIM is to maximize degrees of freedom (DoF) based on network topology information
- Examples show how transmitting signals over multiple channel uses and exploiting the interference pattern can achieve different DoF values through interference alignment
The document provides information about a digital communication systems exam, including questions on various topics in digital communication such as sampling theory, PCM, delta modulation, baseband transmission, digital modulation techniques, error control coding, and spread spectrum.
The exam is divided into two parts (A and B) and contains 10 questions in total. Part A covers topics such as sampling theorem, signal reconstruction, PCM, delta modulation, baseband transmission, and digital modulation formats. Part B focuses on questions related to digital modulation techniques like BPSK, probability of symbol error, DPSK, and spread spectrum modulation. The document provides detailed questions on concepts, derivations, and design problems in digital communication systems.
1. A giant python swallowed an alligator in Everglades National Park, Florida, according to an article in yesterday's New York Times.
2. The article was titled "Invasion of the Giant Pythons" from PBS Nature.
3. The document provided a brief news item about an incident of a giant python eating an alligator in Florida's Everglades National Park.
This document introduces information theory and channel capacity models. It discusses several channel models including the binary symmetric channel (BSC), binary erasure channel, and additive white Gaussian noise channel. It explains how channel capacity is defined as the maximum rate of error-free transmission and derives the capacity for some basic channels. The document also covers channel coding techniques like interleaving that can improve performance by converting burst errors into random errors.
This document provides an overview of pairwise testing. It begins by defining pairwise testing and explaining that it aims to reduce the number of test cases needed while still covering all pairs of input parameters. It then outlines different methods for generating pairwise test cases, including orthogonal Latin squares, Automatic Efficient Test Generator (AETG), In-Parameter-Order (IPO), and genetic algorithms. The document compares the size of test sets generated by different algorithms and lists several pairwise testing tools. It concludes by mentioning additional references and resources on the topic of pairwise testing.
Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not
obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an
adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering
number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional
feature space using gaussian kernel and clustering in the feature space. The Matlab simulation
results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results
1. The document discusses RNA synthesis and processing, including the different types of RNA (mRNA, rRNA, tRNA), the process of transcription, initiation, elongation, and termination.
2. It also covers RNA processing after transcription, including 5' capping, polyadenylation, splicing, and modifications to tRNA, rRNA and other non-coding RNAs.
3. The clinical applications of understanding RNA synthesis and processing are discussed, such as targets for antibiotics, implications for genetic diseases, and miRNA roles in various human health conditions.
DNA contains genes that code for proteins. During transcription, mRNA is produced by copying DNA in the nucleus. The mRNA then transports the genetic code to the cytoplasm for translation at the ribosome. Translation is the process where tRNA brings amino acids to the ribosome according to the mRNA codons to produce a protein, consisting of a chain of amino acids specified by the DNA.
RNA- A polymer of ribonucleotides, is a single stranded structure. There are three major types of RNA- m RNA,t RNA and r RNA. Besides that there are small nuclear,micro RNAs, small interfering and heterogeneous RNAs. Each of them has a specific structure and performs a specific function.
Biochem synthesis of rna(june.23.2010)MBBS IMS MSU
The document summarizes key aspects of RNA synthesis and processing. It discusses that RNA is synthesized from a DNA template in a process called transcription, which is carried out by RNA polymerases. It also describes that in eukaryotes, primary RNA transcripts undergo processing including capping, polyadenylation, and splicing to remove introns and join exons, producing mature mRNA that can then undergo translation to synthesize proteins.
RNA processing in eukaryotes involves multiple steps after transcription in the nucleus. These steps include 5' capping, splicing, editing, and polyadenylation to produce mature messenger RNA that can then be exported and translated into proteins in the cytoplasm. The author holds advanced degrees in biochemistry related to RNA processing.
This document discusses RNA processing and the roles of various proteins involved. It describes how angiogenin regulates hematopoietic stem and progenitor cells by inducing different types of RNA processing - tiRNA to promote quiescence in stem cells and rRNA to promote proliferation in myeloid progenitor cells. This has implications for improving stem cell transplantation outcomes. The document also discusses how PARP proteins regulate gene expression and RNA processing, with PARP inhibitors being used in cancer treatments, and how further understanding their targets could improve cancer therapies.
This document discusses RNA processing in eukaryotic cells. It describes how the primary transcript is modified through capping, polyadenylation, and splicing before being exported to the cytoplasm for protein synthesis. Capping adds a 5' methylguanosine cap. Polyadenylation adds a poly-A tail to the 3' end. Splicing removes introns and joins exons with the help of spliceosomes that contain snRNPs. These processing steps increase mRNA stability and translatability.
RNA polymerase is an enzyme that produces RNA in cells. It was discovered in 1960 and is essential for all organisms. In prokaryotes, a single RNA polymerase synthesizes different RNA types, while eukaryotic RNA polymerase is a multi-subunit enzyme. RNA polymerase I synthesizes rRNA for ribosomes, polymerase II synthesizes pre-mRNA and most snRNA/miRNA, and polymerase III synthesizes tRNA and other small RNAs. The transcription process involves initiation, elongation, and termination stages.
RNA and DNA are nucleic acids that differ in their chemical structure and functions. RNA is typically single-stranded and can form hairpin loops, while DNA is double-stranded. There are various types of RNA that serve different cellular roles. Messenger RNA (mRNA) carries genetic information from DNA to the ribosomes for protein synthesis. Transfer RNA (tRNA) transports amino acids to the ribosome during protein assembly according to the mRNA sequence. Ribosomal RNA (rRNA) is a core component of ribosomes and plays a key role in protein translation.
The document summarizes the process of protein synthesis in three main steps: transcription, translation, and termination. During transcription, RNA polymerase makes an mRNA copy of a DNA sequence. Translation then uses the mRNA to assemble a polypeptide chain via tRNAs and ribosomes. Termination occurs when a stop codon signals the release of the completed protein chain. The central dogma of biology is demonstrated as DNA is transcribed to mRNA which is then translated to protein.
RNA is one of the major biological macromolecules essential for life. It has several types that serve different functions. Messenger RNA (mRNA) carries genetic information from DNA to the ribosomes for protein synthesis. Ribosomal RNA (rRNA) is the catalytic component of ribosomes and is involved in protein translation. Transfer RNA (tRNA) transfers specific amino acids to the growing polypeptide chain during translation.
This document summarizes various cardiovascular drugs used to treat conditions like hypertension, angina, myocardial infarction, shock, and congestive heart failure. It discusses classes of drugs like beta-blockers, ACE inhibitors, calcium channel blockers, vasodilators, and cardiac glycosides. For each drug class, it describes the mechanisms of action, common drugs, clinical uses, contraindications, side effects, and nursing considerations for administration and patient education.
Holistic grading methods evaluate essays as a whole rather than as a sum of parts. A holistic scoring rubric describes the characteristics of excellent, good, and weaker essays. An excellent essay clearly states a position, provides original evidence to support it and refute counterarguments, and makes relationships between ideas clear. A good essay also states a position and addresses counterarguments but may have minor issues. Weaker essays have problems like lack of evidence, organization, or addressing counterarguments.
The document provides details on a course calendar and lecture plan for hidden Markov models (HMM).
1) The course calendar covers topics like Bayesian estimation, Kalman filters, particle filters, hidden Markov models, supervised learning, and clustering algorithms over 14 weeks.
2) The HMM lecture plan introduces discrete-time HMMs and their applications. It covers the three main problems of HMMs - evaluation, decoding, and learning. Evaluation calculates the probability of an output sequence, decoding finds the most probable hidden state sequence, and learning estimates model parameters from training data.
3) The trellis diagram and forward algorithm are described for solving the evaluation problem, while the Viterbi and forward-backward algorithms are mentioned
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Utlization Cat Swarm Optimization Algorithm for Selected Harmonic Elemination...IJPEDS-IAES
The voltage source inverter (VSI) and Current source inverter (CSI) are two
types of traditional power inverter topologies.In this paper selective
harmonic elimination (SHE) Algorithm was impelemented to CSI and results
has been investigated. Cat swarm (CSO) optimization is a new meta-heuristic
algorithm which has been used in order to tuning switching parameters in
optimized value.Objective fuction is reduction of total harmonic
distortion(THD) in inverters output currents.All of simulation has been
carried out in Matlab/Software.
The document discusses triangular norm (t-norm) based kernel functions and their application to kernel k-means clustering. It introduces common kernel functions and describes how t-norms can be used to create new kernel functions. Several parameterized and non-parameterized t-norm based kernel functions are presented. The document then details experiments applying various kernel functions including t-norm kernels to four datasets, evaluating the results using adjusted rand index scores. The best performing kernels for each dataset are identified, with some t-norm kernels performing comparably or better than traditional kernels.
This document discusses using replica exchange Markov chain Monte Carlo (MCMC) with Stan and R to sample from multimodal posterior distributions. It provides an example model with two parameters, samples from the joint distribution using replica exchange MCMC with 10 replicas at different temperatures, and shows trace plots and energy trajectories that indicate good mixing and exchange between replicas. Some discussion points are raised at the end regarding reusing warmup results in Stan and appropriate settings for iteration and warmup lengths in the short MCMC sampling runs between exchange attempts.
Application of Bayesian and Sparse Network Models for Assessing Linkage Diseq...Gota Morota
The document summarizes Gota Morota's master's thesis defense on applying Bayesian and sparse network models to assess linkage disequilibrium in animals and plants. The thesis aims to evaluate linkage disequilibrium (LD) using networks that capture loci associations. It first provides background on standard LD metrics and graphical models. It then describes using a Bayesian network and L1-regularized Markov network to analyze LD in dairy cattle, identifying networks of strongly associated SNPs related to milk protein yield. The thesis concludes the results support LD having a multivariate nature better described by networks than pairwise metrics alone.
Learning Algorithms For Life ScientistsBrian Frezza
This was a very brief introduction to the basics of learning algorithms for life scientists I was asked to give to the incoming first year students at TSRI in the fall of 2005. It covers the very basics of how the algorithms work (sans the complex math) and more importantly, how they can be appropriately understood and applied by chemists and biologists.
This document discusses probabilistic models and string transducers for pairwise sequence alignment and phylogenetic tree construction. It introduces hidden Markov models (HMMs) and the Jukes-Cantor model for nucleotide substitution. UPGMA and neighbor-joining methods are described for building rooted and unrooted phylogenetic trees from distance matrices. Maximum parsimony is also summarized as a method for phylogenetic tree inference based on identifying the smallest number of character state changes.
We apply tensor train (TT) data format to solve an elliptic PDE with uncertain coefficients. We reduce complexity and storage from exponential to linear. Post-processing in TT format is also provided.
Decomposition and Denoising for moment sequences using convex optimizationBadri Narayan Bhaskar
This document summarizes research on using convex optimization techniques like atomic norm minimization to solve problems involving decomposing signals into sparse representations using atoms from predefined dictionaries. It discusses how atomic norm regularization provides a unified framework for problems like sparse recovery, low-rank matrix recovery, and line spectral estimation. It presents theoretical guarantees on exact recovery and convergence rates for atomic norm denoising and shows how to implement it using alternating direction methods and semidefinite programming. Experimental results demonstrate state-of-the-art performance of atomic norm techniques on line spectral estimation tasks.
A walk through the intersection between machine learning and mechanistic mode...JuanPabloCarbajal3
Talk at EURECOM, France.
It overviews regression in several of its forms: regularized, constrained, and mixed. It builds the bridge between machine learning and dynamical models.
This document describes a code structure for calculating and visualizing electric potential and field from point charges. It discusses:
1) Calculating the potential and electric field at grid points due to multiple point charges using superposition principles.
2) Interpolating sparse potential data to generate smooth 2D potential maps.
3) Representing the electric field as vectors showing position, magnitude, and direction originating from point charges.
The code reads charge and position inputs, calculates potentials and fields on a grid, interpolates the potential data, and outputs files to generate vector maps visualizing the electric potential and field.
The document describes implementing the linear convolution of two sequences using MATLAB. Linear convolution involves reflecting one sequence, shifting it, multiplying the sequences element-wise, and summing the results. An example calculates the output of convolving the sequences [1, 2, 3, 1] and [1, 1, 1], yielding the output sequence [1, 3, 6, 6, 4].
In these two lectures, we’re looking at basic discrete time representations of linear, time invariant plants and models and seeing how their parameters can be estimated using the normal equations.
The key example is the first order, linear, stable RC electrical circuit which we met last week, and which has an exponential response.
This document contains 7 questions related to signals and systems from Nehru College of Engineering. The questions cover topics like sampling theorem for low pass signals, sampling a signal at 800Hz, determining Nyquist rates for two signals, finding the input to an LTI system given its step and output response, finding the impulse response of a stable system from a differential equation, describing a continuous time LTI system using a differential equation, and explaining Dirichlet's condition for the existence of Fourier transforms.
ESAI-CEU-UCH solution for American Epilepsy Society Seizure Prediction ChallengeFrancisco Zamora-Martinez
Presentation given at Cyient Insights (Hyderabad, India).
This work presents the solution proposed by Universidad CEU Cardenal Herrera (ESAI-CEU-UCH) at Kaggle American Epilepsy Society Seizure Prediction Challenge. The proposed solution was positioned as 4th at Kaggle competition.
Different kind of input features (different preprocessing pipelines) and different statistical models are being proposed. This diversity was motivated to improve model combination result.
It is important to note that any of the proposed systems use test set for calibration. The competition allow to do this model calibration using test set, but doing it will reduce the reproducibility of the results in a real world implementation.
This document discusses Nyquist's criterion for distortionless transmission of binary signals over a baseband channel. It states that intersymbol interference (ISI) can be eliminated by choosing a transmit filter response P(f) that satisfies the Nyquist criterion. An ideal rectangular pulse shape meets the criterion but is physically unrealizable. A more practical raised cosine pulse is proposed, which introduces a rolloff factor to trade off excess bandwidth for slower decay. The full-cosine case provides additional zero-crossings that aid synchronization but doubles the bandwidth.
1) The document discusses topics related to digital communication systems including sampling theory, PCM, delta modulation, line coding techniques, and spread spectrum.
2) It asks questions about deriving expressions, sketching spectra, block diagrams, and analyzing digital modulation techniques.
3) The exam covers two parts - Part A focuses on digital modulation concepts while Part B covers advanced topics like DPSK, channel coding, and adaptive equalization.
The document discusses the history and development of hidden Markov models (HMMs). It describes key concepts such as HMMs consisting of hidden states that produce observable outputs, and how they can be used to model sequential data. The document also provides examples of applying HMMs to problems such as gene finding, multiple sequence alignment, and protein secondary structure prediction. It summarizes algorithms like forward-backward, Viterbi, and Baum-Welch that are used to train and make predictions from HMMs. Finally, it mentions some popular HMM software tools like HMMER and SAM.
This document discusses sampling and analog-to-digital conversion. It begins by defining sampling as converting a continuous-time signal into a discrete-time signal by taking samples at regular intervals. It then discusses the sampling theorem, which states that a signal must be sampled at least twice as fast as its highest frequency to avoid aliasing. It also covers sampling of bandpass signals and random processes. Finally, it briefly describes common analog pulse modulation techniques like pulse amplitude modulation, pulse width modulation, and pulse position modulation which were used prior to the development of sampling.
Biología de los Tejidos de la cavidad oral, cabeza y cuelloJuan Carlos Munévar
Este documento describe el desarrollo embrionario temprano, incluyendo la segmentación, la gastrulación, la implantación y la formación de estructuras extraembrionarias. También describe el desarrollo de la cabeza, la cara y el cuello, incluyendo la formación de los arcos branquiales, la fusión de los procesos faciales y la formación de las estructuras de la boca y la nariz.
PROYECTO DECRETO
“Por el cual se reglamentan parcialmente las Leyes 9 de 1979, 73 de 1988 y 1805 de 2016, en relación con los componentes anatómicos, y se modifican los artículos 7o, 61 y 88 del Decreto 4725 de 2005” Minsalud República de Colombia
Este documento describe un estudio que buscó identificar las moléculas presentes en el secretoma de células troncales dentales humanas después de la criopreservación. Se analizaron los sobrenadantes de cultivos de células de la pulpa dental, células de la papila apical y otros tipos celulares mediante un panel de citoquinas. Se encontraron varios factores de crecimiento e inmunomoduladores en las células troncales dentales. Los niveles de IL-6, IL-8 y MCP-1 fueron signific
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Stem Cell clinical grade Biology for human therapies. Clase para maestría en Ciencias Básicas Odontológicas en la Universidad El Bosque. Colombia. 2018
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Este documento proporciona información sobre el proceso de publicación de artículos científicos. Explica cómo redactar y estructurar un artículo, seleccionar una revista adecuada, revisar el manuscrito, y navegar el proceso de revisión por pares. También cubre la importancia de la carta de presentación y abordar los comentarios de los revisores. El objetivo final es comprender completamente el proceso de someter un artículo científico para su evaluación y posible publicación.
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Degrada hueso y otros tejidos que han sufrido mineralización secretando enzimas proteolíticas como catepsina K al espacio extracelular.
Este documento describe el Big Data, incluyendo su definición, el gran volumen de datos digitales disponibles, y los desafíos y oportunidades que presenta. Explica que el Big Data no se trata solo de la cantidad de datos, sino de lo que las organizaciones hacen con ellos para obtener conocimiento e información valiosa. También discute brevemente el impacto del Big Data en áreas como la salud, las redes sociales, la industria y la economía.
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Kosmoderma Academy, a leading institution in the field of dermatology and aesthetics, offers comprehensive courses in cosmetology and trichology. Our specialized courses on PRP (Hair), DR+Growth Factor, GFC, and Qr678 are designed to equip practitioners with advanced skills and knowledge to excel in hair restoration and growth treatments.
Promoting Wellbeing - Applied Social Psychology - Psychology SuperNotesPsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
Mercurius is named after the roman god mercurius, the god of trade and science. The planet mercurius is named after the same god. Mercurius is sometimes called hydrargyrum, means ‘watery silver’. Its shine and colour are very similar to silver, but mercury is a fluid at room temperatures. The name quick silver is a translation of hydrargyrum, where the word quick describes its tendency to scatter away in all directions.
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Cell Therapy Expansion and Challenges in Autoimmune DiseaseHealth Advances
There is increasing confidence that cell therapies will soon play a role in the treatment of autoimmune disorders, but the extent of this impact remains to be seen. Early readouts on autologous CAR-Ts in lupus are encouraging, but manufacturing and cost limitations are likely to restrict access to highly refractory patients. Allogeneic CAR-Ts have the potential to broaden access to earlier lines of treatment due to their inherent cost benefits, however they will need to demonstrate comparable or improved efficacy to established modalities.
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Widespread adoption of cell therapies will not only require strong efficacy and safety data, but also adapted pricing and access strategies. At oncology-based price points, CAR-Ts are unlikely to achieve broad market access in autoimmune disorders, with eligible patient populations that are potentially orders of magnitude greater than the number of currently addressable cancer patients. Developers have made strides towards reducing cell therapy COGS while improving manufacturing efficiency, but payors will inevitably restrict access until more sustainable pricing is achieved.
Despite these headwinds, industry leaders and investors remain confident that cell therapies are poised to address significant unmet need in patients suffering from autoimmune disorders. However, the extent of this impact on the treatment landscape remains to be seen, as the industry rapidly approaches an inflection point.
3. DNA sequence
gene
junk DNA
gene
UTR-5' UTR-3'
exon
intron
Promoter module Promoter module
TSS
TFBSTFBS
TATA box
INR DSE
e1 e2 e5e4e3
Distal Promoter Proximal promoter Core promoter
INR DSE
INR = Initiator Region
DSE = DownStream region
TSS = Transcription
Start Site
4. TFBS-Transcription Factor
Binding Site
Short strings (12 to 20
nucleotides long)
spreaded over up to 5kb
before TSS
The string structure select
the protein that will bind on
the basis of Van der Waals
interactions
Van der Waals interactions
-
protein that
is going to bind
example of a Transcription Factor
Binding Sites TFBS
ACCGATTATCA
5. Assembly of the promoter protein
complex of transcription
Transcription factors TF
TFIID
TBP
Transcription factor Binding Sites TFBS
TATA box
INR
TSS
DNA
1st stage
9. known
unknown
TFBS's with the same colour are correlated
The set of all TFBS (for a certain
class of genes, organism or other)
Unknown Known
10. A T G C T C
Protein of the
Promoter complex
A T C C T G
Protein of the
Promoter complex
Example
11. Entropy
Given a probability distribution, we want a function
representing the quantity of information stored in the
distribution.
We define the entropy (H) as:
For the sake of simplicity, we will use from now on
the discrete definition.
dxxpxpH
or
ipipH
i
∫
∑
−=
−=
))(log()(
))(log()(
12. Observed entropy
The real distribution is usually unknown, but
we can replace it by the observed distribution
f(x). The resulting entropy is:
For a multi dimensional probability distribution
it is:
∑−=
x
xfxfxH ))(log()()(
∑ ∑
∑
=
−=
yx y
yx
yxfxyfxf
yxfyxfyxH
,
,
)),(log()|()(
)),(log(),(),(
13. Mutual Information
X and Y are strings of equal length, S={A, C, G, T}, x
and y belong to S
f(x,y) is the relative joint frequency of x,y in X and Y
f(x) is the relative frequency of x in X
f(y) is the relative frequency of y in Y
)()(),(
))](log())(log()),()[log(,(
)
)()(
),(
log(),().(
,
,
yHxHyxH
yfxfyxfyxf
yfxf
yxf
yxfyxI
yx
yx
−−=
−−−=
−=
∑
∑
14. Information divergence
Given two distributions
P and Q
∑∑
∑
−=
=
xx
x
xqxpxpxp
xq
xp
xpQPD
))(log()())(log()(
)
)(
)(
log()(),(
Not for exam
15. A C A T T T A CC A T A G A C A A C T A
A C T T T T A CG A T G G A A A C C T G
X
Y
f(x,y)
6 4 4 6
f(x,y) A C G T
9 A 5 1 2 1
f(x) 5 C 1 3 1 0
1 G 0 0 1 0
5 T 0 0 0 5
Divide by 20 to obtain relative frequencies
Example of calculation
16. Algorithm for finding new
TFBS
1) select a true TFBS (for example ACATTTACCATAGACAACT)
(from a data bank as IUPAC or TRANSFAC) as a probe;
2) shift the probe over a non-coding zone;
3) evaluate step-by-step mutual information I(P,S), where P is
the probe and S is the current adjacent string on the sequence;
4) select the positions (and the corresponding adjacent strings) for
which
I(P,S)> threshold
5) the strings starting from these positions are candidate
TFBS,which need to be validated in vitro.
17. CACTGTGCGACTGTCATTCATCATCCACCGTTGTTAGCACAGGGGTCGATthe same string
TTCGGAACCGGCCTTAAGACGGTGAAGGCGCTACTCATTTAATTGTGTTC
CACTGTGCGTCTGTCATTCATCATCCACCGTTGTTAGCACAGGGGTCGAT1 error
TACTATATAATTGATCGTGTTTTGGCCCGCTACTCATGAAGAGCCGTTCG
CACTGTGCGTCTGTCATTCGTCATCCACCGTTGTTAGCACAGGGGTCGAT2 errors
TAAGGGTATCCAAGTCTGAATACCCCCTGTATTACACTCTCGCTGTCAGT
CACTGTGCGTCTGTCATTCGTCATCCACCATTGTTAGCATAGGGGTCGAC5 errors
CATTATCGAGGACAGTGATTTGTGGAATGCTTGGCCTTAATACGTCTCTA
GAGTCTCGCAGTCTGATTGATGATGGAGGCTTCTTACGAGACCCCTGCATC<--> G
TCAAAGTCAATTTACAGATTGGCGCCTCATGTAATAACGTTGGCATACTA
GAGTGTGGGAGTGTGATTGATGATGGAGGGTTGTTAGGAGAGGGGTGGATC <-- G
CTTAAGATAACGGACACTTGATTGAGATACGCTCGACGCTATGTCCGGCT
CAGTGTCCGACTGTCATTGATCATCCACGCTTGTTACCAGACGCGTCGATsome C<-> G
ACTCGACATAAGGTTACAGCATGTGGAGTAATGCGGTCGCTAACTACGGG
GTGACACGCTGACAGTAAGTAGTAGGTGGCAACAATCGTGTCCCCAGCTAcomplementar
GCGTGGCGAGCTTAATCCCTGCTGCTCTGAGCAAGGAGGGCGTGTAGAAA
GTGACACGCGGACAGTAAGTAGTAGGTGGCAACAATCGTGTCCCCAGCTAcompl+1error
CAAGGTGACAGAGTATTGAGTGAATCTACAATGTTCGCAGTGCTTTGTCG
GTGACACGCTGACAGTAAGAAGTAGGTGGCAACAATCGTGTCCCCAGCTAcompl+2errors
GCGGTCGCCAATCGTCAAGGAAATGATAGGTCTGATTGGCGTGGCTTAAG
GTGACACGCTGACAGTAAGAAGTAGGTGGAAACAATCGTCTCCCCAGCTGcompl+5errors
GGCGCTAACGAATACTTCAAGGCCCGAAGGATTGGTGTTGATACTAGCCG
CACTGTGCGACTGTCATTCATCATCACACCGTTGTTAGCACAGGGGTCGAT1 letter more
CGTGACCAGATGTCCTTACTCTGAATGTTATGGTATTAAGTGAGGTAGTG
CACTGTGCGACTGTCATTCATCATCCACACCGTTGTTAGCACAGGGGTCGAT2 letters more
GCCCATGAACATACATTCATGACTGTTCAAGCGCACTGGACCACTCGTTC
CACTGTGCGACTGTCATTCATCATCCATCACCGTTGTTAGCACAGGGGTCGAT3 letters more
CACTGTGCGACTGTCATTCATCATCCACCGTTGTTAGCACAGGGGTCGATprobe
Example
18. 1 error
2 errors
5 errors
C becomes G
C and G exchanged complementary
complementary+1error
complementary+2errors
complementary+5errors
the same string
4 C become G and 5 G become C
0.2
0.4
0.6
0.8
1
1 letter more
2 letters more
3 letters
more
Detected values for I(P,S)
19. Conclusions:
Use Mutual information as a tool to capture strings
that are correlated to a true TFBS used as a probe.
validate in vitro the candidates so obtained
This is more flexible than the use of Hamming or
Levenshtein distance, since correlated strings
could be very distant one another
Drawbacks:
1. the method need a precise calibration of the
threshold
2. Does not include gaps
21. daf-19 Binding Sites in C. elegans
GTTGTCATGGTGAC
GTTTCCATGGAAAC
GCTACCATGGCAAC
GTTACCATAGTAAC
GTTTCCATGGTAAC
che-2
daf-19
osm-1
osm-6
F02D8.3
-150 -1
22. The (l,d) Planted Motif Problem
Generate a random length l consensus
sequence C.
Generate 20 instances, each differing from C
by d random mutations.
Plant one at a random position in each of
N=20 random sequences of length n=600.
Can you find the planted instances?
24. Random Projection Algorithm
Buhler and Tompa (2001)
Guiding principle: Some instances of a motif
agree on a subset of positions.
Use information from multiple motif instances
to construct model.
ATGCGTC
...ccATCCGACca...
...ttATGAGGCtc...
...ctATAAGTCgc...
...tcATGTGACac... (7,2) motif
x(1)
x(2)
x(5)
x(8)
=M
25. k-Projections
Choose k positions in string of length l.
Concatenate nucleotides at chosen k
positions to form k-tuple.
In l-dimensional Hamming space, projection
onto k dimensional subspace.
ATGGCATTCAGATTC TGCTGAT
l = 15 k = 7
P
P = (2, 4, 5, 7, 11, 12, 13)
26. Random Projection Algorithm
Choose a projection by
selecting k positions
uniformly at random.
For each l-tuple in input
sequences, hash into
bucket based on letters
at k selected positions.
Recover motif from
bucket containing
multiple l-tuples.
Bucket TGCT
TGCACCT
Input sequence x(i):
…TCAATGCACCTAT...
27. Example
l = 7 (motif size) , k = 4 (projection size)
Choose projection (1,2,5,7)
GCTC
...TAGACATCCGACTTGCCTTACTAC...
Buckets
Input Sequence
ATGC
ATCCGAC
GCCTTAC
28. Hashing and Buckets
Hash function h(x) obtained from k positions
of projection.
Buckets are labeled by values of h(x).
Enriched buckets: contain at least s l-tuples,
for some parameter s.
ATTCCATCGCTCATGC
29. Frequency Matrix Model From
Bucket
025.025.010
025.105.00
10025.25.00
05.05.25.01
T
G
C
A
Frequency matrix WATGC
ATCCGAC
ATGAGGC
ATAAGTC
ATGTGAC
Refined matrix W*
EM algorithm
30. Motif Refinement
How do we recover the motif from the
sequences in the enriched buckets?
k nucleotides are known from hash value of
bucket.
Use information in other l-k positions as
starting point for local refinement scheme,
e.g. EM or Gibbs sampler
Local refinement algorithm
ATGCGTC
Candidate motif
ATGC
ATCCGAC
ATGAGGC
ATAAGTC
ATGTGAC
31. Expectation Maximization (EM)
S = { x(1), …, x(N)} : set of input sequences
Given:
W = An initial probabilistic motif model
P0 = background probability distribution.
Find value Wmax that maximizes likelihood ratio:
)|Pr(
)|Pr(
0
max
PS
WS
EM is local optimization scheme. Requires
starting value W
32. EM Motif Refinement
For each bucket h containing more than s
sequences, form weight matrix Wh
Use EM algorithm with starting point Wh to obtain
refined weight matrix model Wh
*
For each input sequence x(i), return l tuple y(i) which
maximizes likelihood ratio:
Pr(y(i) | Wh
*
)/ Pr(y(i) | P0).
T = {y(1), y(2), …, y(N)}
C(T ) = consensus string
33. What Is the Best Motif?
Compute score S for each motif:
Generate W, an initial PSSM from the returned
l-mers {y(1), y(2), …, y(N)}
Return motif with maximal score
∑=
i PiyP
WiyP
Score
)|)((
)|)((
log
0
34. Iterations
Single iteration.
Choose a random k-projection.
Hash each l-mer x in input sequence into bucket
labelled by h(x).
From each bucket B with at least s sequences, form
weight matrix model, and perform EM/Gibbs sampler
refinement.
Candidate motif is the best one found from refinement
of all enriched buckets.
Multiple iterations.
Repeat process for multiple projections.
35. Parameter Selection
Projection size k
Choose k small so several motif instances
hash to same bucket. (k < l - d)
Choose k large to avoid contamination by
spurious l-mers. E > (N (n - l + 1))/ 4k
Bucket threshold s: (s = 3, s = 4)
36. How Many Iterations?
Planted bucket : bucket with hash value h(M),
where M is motif.
Choose m = number of iterations, such that
Pr(planted bucket contains ≥ s sequences in
at least one of m iterations) ≥ 0.95.
Probability is readily computable since
iterations form a sequence of independent
trials.
38. monad patterns
Short contiguous strings
Appear surprisingly many times( in a statistically significant
way)
S =
AGTCAGTCTTGCTAGTCAGTCCGTAATATCCGGATAGAATAATGATC
GTAGCATCGTACGTAGCTATCGATCTGAAGCTAGCAGC
AAGATGTACTAGAGTCAGTCACGTAGCTAGTCAGTCATCTATACGAGAG
TCTCGATGTAGTAGCTATCGATCGTAGCTAGAGTCAGTCCGTAGC
AGCTAGTATCGTAGTGAGCAACATGAGTCAGTCCAGTGCATAA
GTCGTCAGCTCATGAGTCAGTCGCATAGTCAGTC
P = AGTC
39. Introduction
However, many of the actual regulatory
signals are composite patterns.
Groups of monad patterns
Occur relatively near each other
An example of a composite pattern is a dyad
signal.
41. Introduction
A possible approach is to find each part of the
pattern separately and reconstruct the
composite pattern.
However, they often fail to output composite
regulatory patterns consisting of weak monad
parts.
42. Introduction
A better approach would be to detect both parts of a
composite pattern at the same time.
Two steps in the proposed algorithm:
Preprocessing the sample creates a set of ‘virtual’
monads.
Apply an exhaustive monad discovery algorithm to
the ’virtual’ monad problem.
By preprocessing, original problem can be
transformed into a larger monad discovery problem.
43. Monad Pattern Discovery
Canonical pattern lmer
A continuous string of length l
(l, d)-neighbourhood of an lmer P
all possible lmers with up to d mismatches as compared to P
The number of such lmers is :
(l,d)-k patterns
Given a sequence S, find all lmers that occur with up to d
mismatches at least k times in the sample
A variant : the sample is split into several sequence, to find all
lmers, d mismatches, in at least k sequences
A C A3mer:
i
d
i i
l
3
0
∑=
44. Pattern Driven Approach(PDA)
(Prvzner, 2000)
Examine all 4 l patterns of fixed length l in lexical order,
compares each pattern to every lmer in the sample, and
return all (l, d)-k pattern
(Waterman et al., 1984 and Galas et al.,1985)
Bypass excessive time requirement
Most of all 4 l examines not worth since neither these
patterns nor their neighbours appear in the sample
SDA was therefore designed only explores the lmer
appearing in the sample and their neighbours.
45. Sample Driven Approach(SDA)
First initializes a table of size 4l
Each table entry corresponds to a pattern SDA
generate the (l, d)-neighbourhood of lmer
Incremented by a certain amount
After all lmers processed, SDA return all pattern
whose table entries have scores exceed the
threshold
AAAAA 3
AAAAC 1
AAACC 2
… ..
4
l
46. Sample Driven Approach(SDA)
Faster but requires a large 4l
table still
not practical for long pattern in mid 1980
Not mainstream and no tool
(Today gigabytes of RAM memory available thus l
increased without a memory-efficient algorithm)
47. SDA Iterations
First, explore all neighbour of the first lmer from the
sample.
Second, explore all neighbour of the second lmer
If an lmer P belongs to the neighbour of the lmers
appearing at positions i1 ,…ik in the sample info about P
collected at iteration i1 ,…ik .
So the Waterman approach update info about P k times
memory slot for P is occupied during the course time even
if P is not “interesting” lmer
Most of lmers explored are not interesting—waste memory
slot
48. To improve SDA
Better solution:
Collect info about all P at the same time
to remove the need to keep the info in memory
but require a new approach to navigate the space of
all lmers
MITRA runs faster than PDA and SDA, and uses
only a fraction of the memory of the SDA
49. Pattern-finding vs. profile-based
Profile-based is more biologically relevant for
finding motifs in biological samples?
Probably the reason Waterman algorithm not
popular in the last decade
Sagot and colleagues were the first to rebut this
opinion
Develop an efficient version of Waterman’s
50. Pattern-based vs. profile-based
Similarities
Pattern-based generate the profile
Every profile of length l corresponds to a pattern of length
l formed by the most frequent nucleotides in every
position.
Pattern-driven at least as good as profile-based
Even better on simulated samples with implanted patterns
Though profile-implantation model is somehow limited
Today little evidence profile-based perform any better on
either biological or simulated samples
52. Mismatch Tree Algorithm
(MITRA)
MITRA uses a mismatch tree data structure to
split the space of all possible patterns into disjoint
subspaces that start with a given prefix.
For reducing the pattern discovery into smaller
sub-problems.
MITRA also takes advantage of pair-wise
similarity between instances.
53. Splitting Pattern Space
A pattern is called weak if it has less than k
( l ,d )-neighbours in the sample.
A subspace is called weak if all patterns in this
subspace are weak.
54. Splitting pattern space
A pattern is called weak if it has less than k
( l ,d )-neighbours in the sample.
l = 3 …. sample = { AGT, GTA, TAT, ATC, TCA, CAG, AGT, GTT }
d =1 ; k =2
( l ,d )-neighbours in the sample = { GTA, ATC, GTT }
Sequence = AGTATCAGTT
P= GTC
Not weak
55. Splitting pattern space
A pattern is called weak if it has less than k
( l ,d )-neighbours in the sample.
l = 3 …. sample = { AGT, GTA, TAT, ATC, TCA, CAG, AGT, GTT }
d =1 ; k =2
( l ,d )-neighbours in the sample = { CAG }
Sequence = AGTATCAGTT
P= CAG
weak
56. Splitting pattern space
A subspace is called weak if all patterns in this
subspace are weak.
•subspaceA = { AAA, AAT, AAC, AAG ………..AGG }
•subspaceT = { TAA, TAT, TAC, TAG ………..TGG }
•subspaceC = { CAA, CAT, CAC, CAG ………..CGG }
•subspaceGG = { GGA, GGT, GGC, GGG}
Sequence = AGTATCAGTT
57. Question
Input:
S, l, d, k
Output:
All l mers that occur with up to d mismatches
at least k times in the sample.
58. Solution
Naïve :
Test all l mer in the space
If occur with up to d mismatches at least k times
in the sample than output this l mer.
space = { AAA, AAT, AAC, AAG ………..AGG
TAA, TAT, TAC, TAG ………..TGG
CAA, CAT, CAC, CAG ………..CGG
GAA, GAT, GAC, GAG ………..GGG }
sample = { AGT, GTA, TAT, ATC, TCA, CAG, AGT, GTT }
59. Splitting pattern space
if we are looking for patterns of length l we would first
split the space of all l mers into 4 disjoint subspaces.
Subspace of all l mers starting with A,
Subspace of all l mers starting with T,
Subspace of all l mers starting with C,
Subspace of all l mers starting with G,
60. Splitting pattern space
if we are looking for patterns of length l we would first
split the space of all l mers into 4 disjoint subspaces.
Space:
A*
SubspaceA
T* C* G*
61. Splitting pattern space
we further determine whether the subspace
contains a ( l ,d )-k pattern.
Space:
A*
Can’t rule out
62. Splitting pattern space
we further determine whether the subspace
contains a ( l ,d )-k pattern.
Space:
AT*
AA* AC*
AG*
Can rule out
63. Splitting pattern space
we further determine whether the subspace
contains a ( l ,d )-k pattern.
Space:
Can’t rule out
64. Splitting pattern space
we further determine whether the subspace
contains a ( l ,d )-k pattern.
If we can rule out this subspace contains such
a pattern
we stop searching in this subspace;
release the memory slot;
If we can’t rule out this subspace contains
such a pattern
we split this subspace again on the next
symbol;
and repeat;
65. Mismatch tree data structure
A mismatch tree is a rooted tree where each internal
node has 4 branches labeled with a symbol in
{A,C,T,G}
The maximum depth of the tree is l.
Each node in the mismatch tree corresponds to the
subspace of patterns P with a fixed prefix.
Each node contains pointers to all l mers instances
from the sample that are within d mismatches from a
pattern p.
66. Mismatch tree data structure
MITRA start with examining the root node of the
mismatch tree that corresponds to the space of all
patterns.
When examining a node, MITRA tries to prove that it
corresponds to a weak subspace.
If (we can’t prove it)
we expand the node’s children and examine each of
them.
Whenever we reach a node corresponding to a weak
subspace, we backtrack.
The intuition is that many of the nodes correspond
to weak subspaces and can be rule out.
This allows us to avoid searching much of the
pattern space.
67. Mismatch tree data structure
If we reach depth l and the number of instances is
not less than k.
the l mer corresponding to the path from the
root to the leaf .
the pointers from this node correspond to the
instances of this pattern.
68. Example
Consider a very simple example of finding the
pattern of length 4 with up to 1 mismatch and
at least 2 times in the sample S =
“AGTATCAGTT”.
The substrings (4mers) in S are
{ AGTA, GTAT, TATC, ATCA, TCAG,
CAGT, AGTT }
Not for exam
69. A
A
A
k =7
k = 5
0 0 0 0 0 0 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
0 1 1 0 1 1 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
1 2 1 1 2 1 1
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
2 2 2 2 2
A T A C A
G A T A G
T T C G T
A C A T T
k = 0
C
2 2 1 2 2
A T A C A
G A T A G
T T C G T
A C A T T
k = 1
G 2 2 2 1 2
A T A C A
G A T A G
T T C G T
A C A T T
k = 1
1 1 2 2 1
A T A C A
G A T A G
T T C G T
A C A T T
T
k = 3
A 1 2 2
A T A
G A G
T T T
A C T
k = 1
C
2 1 2
A T A
G A G
T T T
A C T
k = 1
G 2 2 2
A T A
G A G
T T T
A C T
k = 0
2 2 1
A T A
G A G
T T T
A C T
T
k = 1
70. A
k =7
0 0 0 0 0 0 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
0 1 1 0 1 1 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
G
k = 3
0 2 2 1 2 2 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
0 2 0
A A A
G T G
T C T
A A T
T
k = 2
A 0 1
A A
G G
T T
A T
k = 2
Output: AGTA C
1 1
A A
G G
T T
A T
k = 2
AGTC
G 1 1
A A
G G
T T
A T
k = 2AGTG
1 0
A A
G G
T T
A T
T
k = 2
AGTT
T
71. Overall complexity
Space =
Time =
TTGACTA
TGACTAT
GACTATG
ACTATGA
0000000
A
G
T
T
O(|S|)
O(l)
O(O(ll22
× |S|)× |S|)
O(4O(4ll
× |S|)× |S|)
.
.
.
.
.
.
.
.
.
l
Number of nodes = O(4l
)
l
TTGACTA
TGACTAT
GACTATG
ACTATGA
0110110
O(|S|)
– Number of comparisons in each node = O(|S|)Number of comparisons in each node = O(|S|)
72. Take a Closer Look
In mismatch tree algorithm, we can not start
ruling out a node until traverse to depth .
A
A
k =7
k = 5
0 0 0 0 0 0 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
0 1 1 0 1 1 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
1 2 1 1 2 1 1
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
d +1
73. MITRA Graph
Information about pairwise similarities between
instances of the pattern can significantly
the sample-driven approach.
The graph that is constructed to model this
pairwise similarity is called MITRA-Graph
speed up
74. MITRA Graph
Given a pattern P and sample S we can construct
a graph G(P, S) where each vertex is an lmer in
the sample and there is an edge connecting two
lmers if P is within d mismatches from both
lmers.
ACA
(d=3)
TAA
(d=1)
AAC (d=1)
P = TAC
S = TAACA
75. MITRA Graph
For an (l,d) – k pattern P the corresponding graph
contains a clique of size k.
ACA
(d=3)
TAA
(d=1)
AAC (d=1)
P = AAA
S = TAACA
76. MITRA Graph
Given a set of patterns P and a sample S, define a
graph G(P , S) whose edge set is a union of edge
sets of graphs G(P, S) for P∈P .
Each vertex of G(P , S) is an lmer in the sample
and there is an edge connecting two lmers if there
is a pattern P∈P that is within d mismatches
from both lmers.
If for a subspace of patterns we can rule out an
existence of a clique of size k, then the subspace
has no (l,d)-k
77. The WINNOWER Algorithm
The WINNOWER algorithm by Pevzner and
Sze (2000) constructs the following graph:
Each lmer in the sample is a vertex, and an edge
connects two vertices if the corresponding lmers
have less than d mismatches.
Instances of a (l,d)-k pattern form a clique of
size k in this graph.
78. The WINNOWER Algorithm
(con’t)
Since clique are difficult to find, WINNOWER
takes the approach of trying to remove edges that
do not corresponding to a clique.
k = 4
79. Improvements by MITRA-Graph
1. Construct a graph at each node in the mismatch
tree.
A
0 1 1 0 1 1 0
A G T A T C A
G T A T C A G
T A T C A G T
A T C A G T T
81. Improvements by MITRA-Graph
3. If no potential clique remains, rule out the
subspace corresponding to the node and
backtrack.
A
A
82. Improvements by MITRA-Graph
4. If we cannot rule out a clique, split the subspace
of patterns and examine the child nodes
A
83. MISMATCH TREE ALGORITHM —
Improvements over WINNOWER
At each node of the tree, we remove edges
by computing the degree of each vertex.
If the degree of the vertex is less than k-1,
we can remove all edges incident to it since
we know it is not part of a clique.
We repeat this procedure until we cannot
remove any more edges.
If the number of edges remaining is less than
the minimum number of edges in a clique,
we can rule out the existence of a clique and
backtrack.
84. MISMATCH TREE ALGORITHM —
Improvements over WINNOWER
The problem with this approach is how to
efficiently construct the graph at each node in
the mismatch tree.
Instead of constructing the graph from scratch,
we construct it based on the graph at the
parent node
an edge connecting two l mers
the first l mer matches the prefix of the pattern
subspace with d1 mismatches
the second l mer matches with d2 mismatches
85. MISMATCH TREE ALGORITHM —
Improvements over WINNOWER
the number of mismatches between the tail of
the first and the second l mers as m.
The edge between these two l mers exists in
the pattern subspace if and only if d1 <= d,
d2 <= d and d1+d2+m <= 2d.
the first lmer
the second lmer
The prefix of the
pattern subspace
86. MISMATCH TREE ALGORITHM —
Improvements over WINNOWER (cont’d)
In the root node since d1 = d2 = 0, an edge exists only if
m <= 2d which is the equivalent graph to
WINNOWER.
With moving down the tree, the condition becomes
much stronger than the WINNOWER.
We can compute the edges of a node based on the
edges of the node’s parents by keeping track of the
quantities d1, d2, and m for each edge.
87. MISMATCH TREE ALGORITHM —
Improvements over WINNOWER
To summarize, the MITRA-Graph algorithm works as
follows
We first compute the set of edges at the root node by
performing pairwise comparisons between all l mers
due to d1 = d2 = 0.
We traverse the tree in a depth first order, passing on
the valid edges and keeping track of the quantities d1,
d2, and m for each of them.
At each node, we prune the graph by eliminating any
edges incident to vertices that have degrees of less
than k-1.
If there are less than the minimum number of edges for
a clique, we backtrack.
If we reach a leaf of the tree (depth l), then we output
the corresponding pattern.
89. DISCOVERING DYNAD SIGNALS
For dyad signals, we are interested in
discovering two monads that occur a certain
length apart
We use the notation (l1-(s1,s2)-l2,d)-k pattern to
denote a dyad signal
s s sl1 l1 l1l2 l2 l2
90. DISCOVERING DYNAD SIGNALS
The MITRA-Dyad algorithm casts the dyad
discovery problem into a monad discovery
problem by preprocessing the input and
creating a “virtual” sample to solve the
(l1+l2,d)-k monad pattern discovery problem in
this sample
For each l1mer in the sample and for each s in
[s1,s2], we create an l1+l2 mer which is the l1mer
concatenated with the l2 mer upstream s
nucleotides of the l1mer.
91. DISCOVERING DYNAD SIGNALS
The number of elements in the “virtual” sample
will be approximately (s1-s2+1) times larger.
An (l1+l2,d)-k pattern in the “virtual” sample will
correspond to a (l1-(s1,s2)-l2,d)-k pattern in the
original sample, and we can easily map the
solution from the monad problem to the dyad
one.
An important feature of MITRA-Dyad is an
ability to search for long patterns.
92. DISCOVERING DYNAD SIGNALS
If the range s1-s2+1 of acceptable distances
between monad parts in a composite pattern
is large, the MITRA-Dyad algorithm becomes
inefficient
A simple approach to detect these patterns is
to generate a long ranked list of candidate
monad patterns using MITRA.
Then check each occurrence of each pair from
the list to see if they occur within the
acceptable distance.