- The document discusses using a sequential probability ratio test (SPRT) for sparse signal detection from compressed measurements. SPRT allows observations to continue until sufficient evidence is accumulated to decide between two hypotheses.
- It outlines how to apply SPRT to the problem by deriving the likelihood ratio test statistic and decision thresholds based on desired false alarm and detection probabilities. Performance is characterized by bounding the probability of error based on properties of compressed sensing measurements.
- Simulation results show decreasing decision time with higher compression ratios and numbers of observations, consistent with theoretical predictions. Future work includes refining the analysis and extending it to random sparse signals.
Transportation Problem In Linear ProgrammingMirza Tanzida
This work is an assignment on the course of 'Mathematics for Decision Making'. I think, it will provide some basic concept about transportation problem in linear programming.
Transportation Problem In Linear ProgrammingMirza Tanzida
This work is an assignment on the course of 'Mathematics for Decision Making'. I think, it will provide some basic concept about transportation problem in linear programming.
How to 2D plots in Matlab. Easy steps to graph mathematical functions.
You have to define your interval of interest and consider a step in your independent vector, then you have to define your function and use an appropriate 2D built-in function.
More information and examples:
http://matrixlab-examples.com/matlab-plot-2tier.html
Slides for the 2016/2017 edition of the Data Mining and Text Mining Course at the Politecnico di Milano. The course is also part of the joint program with the University of Illinois at Chicago.
Solve nonlinear equations using bracketing methods: Bisection and False Position
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
How to 2D plots in Matlab. Easy steps to graph mathematical functions.
You have to define your interval of interest and consider a step in your independent vector, then you have to define your function and use an appropriate 2D built-in function.
More information and examples:
http://matrixlab-examples.com/matlab-plot-2tier.html
Slides for the 2016/2017 edition of the Data Mining and Text Mining Course at the Politecnico di Milano. The course is also part of the joint program with the University of Illinois at Chicago.
Solve nonlinear equations using bracketing methods: Bisection and False Position
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Lec-17: Sparse Signal Processing & Applications [notes]
Sparse signal processing, recovery of sparse signal via L1 minimization. Applications including face recognition, coupled dictionary learning for image super-resolution.
Covariance matrices are central to many adaptive filtering and optimisation problems. In practice, they have to be estimated from a finite number of samples; on this, I will review some known results from spectrum estimation and multiple-input multiple-output communications systems, and how properties that are assumed to be inherent in covariance and power spectral densities can easily be lost in the estimation process. I will discuss new results on space-time covariance estimation, and how the estimation from finite sample sets will impact on factorisations such as the eigenvalue decomposition, which is often key to solving the introductory optimisation problems. The purpose of the presentation is to give you some insight into estimating statistics as well as to provide a glimpse on classical signal processing challenges such as the separation of sources from a mixture of signals.
Digital Signal Processing[ECEG-3171]-Ch1_L02Rediet Moges
This Digital Signal Processing Lecture material is the property of the author (Rediet M.) . It is not for publication,nor is it to be sold or reproduced
#Africa#Ethiopia
Reinforcement learning: hidden theory, and new super-fast algorithms
Lecture presented at the Center for Systems and Control (CSC@USC) and Ming Hsieh Institute for Electrical Engineering,
February 21, 2018
Stochastic Approximation algorithms are used to approximate solutions to fixed point equations that involve expectations of functions with respect to possibly unknown distributions. The most famous examples today are TD- and Q-learning algorithms. The first half of this lecture will provide an overview of stochastic approximation, with a focus on optimizing the rate of convergence. A new approach to optimize the rate of convergence leads to the new Zap Q-learning algorithm. Analysis suggests that its transient behavior is a close match to a deterministic Newton-Raphson implementation, and numerical experiments confirm super fast convergence.
Based on
@article{devmey17a,
Title = {Fastest Convergence for {Q-learning}},
Author = {Devraj, Adithya M. and Meyn, Sean P.},
Journal = {NIPS 2017 and ArXiv e-prints},
Year = 2017}
Session (1) of recruitment campaign.
-The admission of NU is open now.
For any information:
* Website: http://en.nu.edu.eg/
*Admission email: admission@nu.edu.eg
*Seif's email: m.seif@nu.edu.eg
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
2. Outline
November 2017The University of Arizona
• Motivation
• Preliminaries on Compressive Sensing
• Sequential Probability Ratio Test: Recap
• Work Discussion
2
3. Compressive Sensing
November 2017The University of Arizona 3
s
sparse signalN ⇥ 1
K (=3) non-zero
elements
Sparsity of order K
M ⇥ N random matrix
Gaussian distribution
=
y
Dimensionality Reduction
M ⇥ 1 measurements
K < M << N
Scanning the support of the
signal has exponential
complexity!
4. How to recover the sparse signal?
November 2017The University of Arizona 4
RN
dimensional space
s
{s0
: y = s0
}
(1 )ksk2
2 k sk2
2 (1 + )ksk2
2
Restricted Isometry Property:
Gaussian distribution works!
M 2K log
✓
N
M
◆
Required number of measurements:
RM
s
5. How to recover the sparse signal? (Cont’d)
November 2017The University of Arizona 5
RN
dimensional space
s
{s0
: y = s0
}
Question: How to estimate the signal?
l2 norm recovery
ˆs
Not accurate!
ˆs = arg min
y= s0
ksk2
ksk2
2 = |s1|2
+ |s2|2
+ · · · + |sN |2
Where,
RM
6. How to recover the sparse signal? (Cont’d)
November 2017The University of Arizona 6
RN
dimensional space
s
{s0
: y = s0
}
Question: How to estimate the signal?
ˆsl1 norm recovery
ˆs = arg min
y= s0
ksk1
ksk1 = |s1| + |s2| + · · · + |sN |
Where,
RM
7. Stopping Problem: Recap
November 2017The University of Arizona
• Stopping problems are a simple but important class of learning problems.
•In this problem class, information arrives over time, and we have to
choose whether to view the information or stop and make a decision.
7
Event Detector
t=0 t=1 t=2 t=3
. . .
t=10
Input Signal
Sudden Change in observation
t=0 t=1 t=2 t=3
. . .
t=10
Ideal case: Stop observing and detect the change accurately!
Output Signal
8. Solution of the problem
November 2017The University of Arizona 8
⇢0
0
Risk
0.5
1 ⇢0
0 ⇢0
0
Risk is a concave function
⇢L ⇢U
Stop and decide H1Stop and decide H0
Continue updating priors
9. Solution of the problem (Cont’d)
November 2017The University of Arizona 9
• Now we are interested to obtain ⇢L
, ⇢U
• The updated prior is
⇢n+1
0 =
Ln
(Sn
)
Ln(Sn) + ⇢0/(1 ⇢0)
Ln
(Sn
) =
nY
k=1
P1(Wk
)
P0(Wk)
• The likelihood ratio is defined as
10. Solution of the problem (Cont’d)
November 2017The University of Arizona 10
• Determining if
⇢n+1
0 =
Ln
(Sn
)
Ln(Sn) + ⇢0/(1 ⇢0)
⇢n+1
0 (Sn
) ⇢L
or ⇢n+1
0 (Sn
) ⇢U
is the same as testing
Ln
(Sn
) Aor Ln
(Sn
) B
• Why?
Quasi linear function
0
Increasing function for Ln
(Sn
) 0
11. Solution of the problem (Cont’d)
November 2017The University of Arizona 11
• The new bounds A and B are obtained as
A =
⇢n
0 ⇢L
(1 ⇢n
0 )(1 ⇢L)
B =
⇢n
0 ⇢U
(1 ⇢n
0 )(1 ⇢U )
• Now the decision rule is
Ln
(Sn
) =
8
><
>:
B stop and chooseY n
= 1
A stop and choose Y n
= 0
otherwise continue observing
12. Solution of the problem (Cont’d)
November 2017The University of Arizona 12
• Since getting A, B exactly is difficult
P⇡
F ⇡
1 A
B A
P⇡
M ⇡
A(B 1)
B A
Wald’s approximation
• Then for an acceptable P⇡
F , P⇡
M
A =
P⇡
M
1 P⇡
F
B =
1 P⇡
M
P⇡
F
14. Hypothesis Testing
November 2017The University of Arizona 14
Random Deterministic (Today’s Talk)
H1 : yi = s + ni
H0 : yi = ni noise only
signal + noise
15. Hypothesis Testing
November 2017The University of Arizona 15
Likelihood functions:
f(yi|H0) =
exp( 1
2 yT
i ( 1 t
) 1
yi)
| 1 |1/2(2⇡)M/2
f(yi|H1) =
exp( 1
2 (yi s)T
( 1 t
) 1
(yi s)
| 1 |1/2(2⇡)M/2
=
1
2
(noise variance)
Typo: T
16. Sequential Probability Ratio Test
November 2017The University of Arizona 16
• We need to compute the likelihood function
Ln
(Sn
) =
nY
i=1
f1(yi|H1)
f0(yi|H0)
Ln
(Sn
) =
8
><
>:
B stop and chooseY n
= 1
A stop and choose Y n
= 0
otherwise continue observing
• Remember the decision rule
17. Sequential Probability Ratio Test
November 2017The University of Arizona 17
• After algebraic simplifications
⇤(y) 1 H1conclude
⇤(y) 2 conclude H0
2 ⇤(y) 1 continue observing
Decision statistic
• Where,
⇤(y) =
nX
i=1
yT
i ( T
) 1
s
1 = 2 log(B) + n( s)T
( T
) 1
s
2 = 2 log(A) + n( s)T
( T
) 1
s
18. Performance Characterization
November 2017The University of Arizona 18
• Average probability of error
Pe = P(H0)Pfa + P(H1)(1 Pd)
Pfa = P(⇤(y) 1|H0)
Pd = P(⇤(y) 1|H1)
• We assume,
P(H0) = P(H1) = 1/2
• We get,
ˆP = T
( T
) 1
,
False alarm probability
Detection probability
Pe = Q
✓
1
2
r
n
1
kˆPsk
◆
A = B = 1,
In SPRT, PfaPd and
are predefined
19. Performance Characterization (Cont’d)
November 2017The University of Arizona 19
Pe = Q
✓
1
2
r
n
1
kˆPsk
◆
This expression does not
show the impact of
compressed measurement!
stable embedding Theorem
Davenport, Mark A., et al. "Signal processing with compressive
measurements." IEEE Journal of Selected Topics in Signal Processing 4.2
(2010): 445-460.
Suppose that
r
N
M
ˆP provides a -stable embedding property.
It satisfies!
Then for any
deterministic signal s, the probability of error has the following bounds:
Q
✓
p
1 +
p
n
2
r
M
N
ksk2
p
1
◆
Pe Q
✓
p
1
p
n
2
r
M
N
ksk2
p
1
◆
Theorem:
20. Performance Characterization (Cont’d)
November 2017The University of Arizona 20
• Then, approximately
Pe ⇡ Q
✓p
n
2
r
M
N
ksk2
p
1
◆
Compression ratio < 1
Time
p
SNR
@ SNR = 3 dB
Comment: monotonically decreasing function of compression ratio and number of time.
21. Simulation Results
November 2017The University of Arizona 21
Less measurements, more delay!
Compression ratio (CR) =
M
N
Sparsity order (K) = 5
Signal dimension (N) =100
Number of measurements
Pd = 0.1, Pfa = 0.1
Monte-Carlo Simulation (number of iterations = 10000)
22. Simulation Results
November 2017The University of Arizona 22
Compression ratio (CR) =
M
N
Sparsity order (K) = 5
Signal dimension (N) =50
Number of measurements
Pd = 0.1, Pfa = 0.1
Monte-Carlo Simulation (number of iterations = 100) (lack of time)
Reconstruction using l1 norm algorithm
min
s
ksk1
s.t. ky sk2
P(ˆs 6= s)
M = 10
23. Future Work
November 2017The University of Arizona
• Refining the results
• Studying the SPRT mechanism for random signals
• Expecting a research paper