Classification of mathematical modeling,
Classification based on Variation of Independent Variables,
Static Model,
Dynamic Model,
Rigid or Deterministic Models,
Stochastic or Probabilistic Models,
Comparison Between Rigid and Stochastic Models
Classification of mathematical modeling,
Classification based on Variation of Independent Variables,
Static Model,
Dynamic Model,
Rigid or Deterministic Models,
Stochastic or Probabilistic Models,
Comparison Between Rigid and Stochastic Models
Data Analysis: Statistical Methods: Regression modelling, Multivariate Analysis - Classification: SVM & Kernel Methods - Rule Mining - Cluster Analysis, Types of Data in Cluster Analysis, Partitioning Methods, Hierarchical Methods, Density Based Methods, Grid Based Methods, Model Based Clustering Methods, Clustering High Dimensional Data - Predictive Analytics – Data analysis using R.
The main goal of statistical phylogenetics is to reconstruct accurate phylogenies by means of comparison of nucleotide or protein sequences (i.e. DNA or Proteomics analysis). However, recent advances have shown that phylogenetics is not only related to taxonomy (i.e. data/species classification into categories) since different regions in nucleotide and protein sequences are subject to different evolutionary pressures or strains. Moreover, it is now apparent that different sequences accumulate substitutions at different rates (i.e. presence of inhomogeneities along sequences).
Structural and functional constraints vary across sites of a protein. In other words, some protein sites may evolve slowly since most mutations ocurring at this particular site have low probabilities of being transmitted to descendants. For example, residues near the core of the molecule evolve under different processes than those exposed at the surface. The most dramatic example of this is related to the protein binding site dynamics, where the response of the cell depends on the binding nature of the cell receptors. In this case, one mutation in the core of the protein may turn an hallosterinc binding site into an orthosteric binding site and, therefore, the full response of the cell to a given receptor may be completely changed (for example, a severe infection turning into haemodynamic shock).
From what has been said so far, it becomes apparent that the structural and functional constraints that shape protein evolution also affect substitution processes at the nucleotide level and vice versa. In this regard, two thirds of the nucleotide changes at the third codon position do not modify the amino acid translated (synonimous changes), whilst the mutations that take place at the second position systematically change the amino acid translated (non-synonimous changes). Also only 10\% of changes at the first codon position are synonimous so it can be concluded that evolutionary pressure varies depending on the constraints already present at the protein level.
A simple approach to model this evolutionary feature is to allow the substition rates to vary across amino acid or nucleotide sites of the sequence. However, the estimation of the rate of change for each site of the alignment is impossible due to a combinatory explosion. In order to overcome this problem it is assumed that site rates are unknown but comply with a probabilistic distribution whose parameters or shape are estimated from the data.
The structure of the genetic code is also responsible for other evolutionary patterns which are more complex than variations in rates across codon positions. Synonimous and non-synonimous mutations have varying probabilities of becoming `fixed' in a given population, which depends on the selective forces that act on the corresponding amino acids.
Hello,
This is Tahsin Ahmed Nasim. I'm a student of Civil Engineering. My Own MARKOV CHAINS Presentation.
This is the part of Probability of Statistic.
Power System Simulation: History, State of the Art, and ChallengesLuigi Vanfretti
This talk will give an overview of power system simulation technology through several decades, aiming to provide an understanding of the modeling philosophy and approach that has lead to the state of the art in (domain specific) power system simulation tools. This historical perspective will contrast the de facto proprietary software development method used by the power engineering community, against the open source development model. Aspects of resistance to change particular to the power system engineering community will be highlighted.
Given this particular context, power system simulation faces enormous challenges to adapt in order to satisfy simulation needs of both cyber-physical and sustainable system challenges. Such challenges will be highlighted during the talk.
There is, however, an opportunity for disruptive change in power system simulation technology emerging for the EU Smart Grid Mandate M/490, which requires "a set of consistent standards, which will support the information exchange (communication protocols and data models) and the integration of all users into the electric system operation." These regulatory aspects will be explained to highlight the importance of collaboration between the power system domain and computer system experts.
Open modeling and simulation standards may have a large role to play in the development of the European Smart Grid which will have to overcome challenges related to the design, operation and control of cyber-physical and sustainable electrical energy systems. To contribute to this role, the KTH SmarTS Lab research group has been applying the standardized Modelica language and the FMI standard for model exchange in order to couple the domain specific data exchange model (CIM) with the powerful and modern simulation technologies developed by the Modelica community. These efforts will be also discussed.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Data Analysis: Statistical Methods: Regression modelling, Multivariate Analysis - Classification: SVM & Kernel Methods - Rule Mining - Cluster Analysis, Types of Data in Cluster Analysis, Partitioning Methods, Hierarchical Methods, Density Based Methods, Grid Based Methods, Model Based Clustering Methods, Clustering High Dimensional Data - Predictive Analytics – Data analysis using R.
The main goal of statistical phylogenetics is to reconstruct accurate phylogenies by means of comparison of nucleotide or protein sequences (i.e. DNA or Proteomics analysis). However, recent advances have shown that phylogenetics is not only related to taxonomy (i.e. data/species classification into categories) since different regions in nucleotide and protein sequences are subject to different evolutionary pressures or strains. Moreover, it is now apparent that different sequences accumulate substitutions at different rates (i.e. presence of inhomogeneities along sequences).
Structural and functional constraints vary across sites of a protein. In other words, some protein sites may evolve slowly since most mutations ocurring at this particular site have low probabilities of being transmitted to descendants. For example, residues near the core of the molecule evolve under different processes than those exposed at the surface. The most dramatic example of this is related to the protein binding site dynamics, where the response of the cell depends on the binding nature of the cell receptors. In this case, one mutation in the core of the protein may turn an hallosterinc binding site into an orthosteric binding site and, therefore, the full response of the cell to a given receptor may be completely changed (for example, a severe infection turning into haemodynamic shock).
From what has been said so far, it becomes apparent that the structural and functional constraints that shape protein evolution also affect substitution processes at the nucleotide level and vice versa. In this regard, two thirds of the nucleotide changes at the third codon position do not modify the amino acid translated (synonimous changes), whilst the mutations that take place at the second position systematically change the amino acid translated (non-synonimous changes). Also only 10\% of changes at the first codon position are synonimous so it can be concluded that evolutionary pressure varies depending on the constraints already present at the protein level.
A simple approach to model this evolutionary feature is to allow the substition rates to vary across amino acid or nucleotide sites of the sequence. However, the estimation of the rate of change for each site of the alignment is impossible due to a combinatory explosion. In order to overcome this problem it is assumed that site rates are unknown but comply with a probabilistic distribution whose parameters or shape are estimated from the data.
The structure of the genetic code is also responsible for other evolutionary patterns which are more complex than variations in rates across codon positions. Synonimous and non-synonimous mutations have varying probabilities of becoming `fixed' in a given population, which depends on the selective forces that act on the corresponding amino acids.
Hello,
This is Tahsin Ahmed Nasim. I'm a student of Civil Engineering. My Own MARKOV CHAINS Presentation.
This is the part of Probability of Statistic.
Power System Simulation: History, State of the Art, and ChallengesLuigi Vanfretti
This talk will give an overview of power system simulation technology through several decades, aiming to provide an understanding of the modeling philosophy and approach that has lead to the state of the art in (domain specific) power system simulation tools. This historical perspective will contrast the de facto proprietary software development method used by the power engineering community, against the open source development model. Aspects of resistance to change particular to the power system engineering community will be highlighted.
Given this particular context, power system simulation faces enormous challenges to adapt in order to satisfy simulation needs of both cyber-physical and sustainable system challenges. Such challenges will be highlighted during the talk.
There is, however, an opportunity for disruptive change in power system simulation technology emerging for the EU Smart Grid Mandate M/490, which requires "a set of consistent standards, which will support the information exchange (communication protocols and data models) and the integration of all users into the electric system operation." These regulatory aspects will be explained to highlight the importance of collaboration between the power system domain and computer system experts.
Open modeling and simulation standards may have a large role to play in the development of the European Smart Grid which will have to overcome challenges related to the design, operation and control of cyber-physical and sustainable electrical energy systems. To contribute to this role, the KTH SmarTS Lab research group has been applying the standardized Modelica language and the FMI standard for model exchange in order to couple the domain specific data exchange model (CIM) with the powerful and modern simulation technologies developed by the Modelica community. These efforts will be also discussed.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
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.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
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.
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2. Matrix Geometric Method
• The matrix geometric method is a mathematical technique that can
be used to analyze the behavior of certain types of systems, such as
Markov chains and queuing systems. The method involves
representing the system as a matrix, and using matrix algebra to study
the long-term behavior of the system.
3. • One of the key features of the matrix geometric method is that it
allows for the analysis of systems with an infinite state space, such as
systems with a countably infinite number of states or systems with a
continuous state space. This makes the method particularly useful for
studying systems with complex behavior that cannot be easily
analyzed using other techniques.
4. • In addition to its use in analyzing systems, the matrix geometric
method has also been applied to other areas of mathematics,
including the study of differential equations and the solution of linear
systems of equations.
• Overall, the matrix geometric method is a powerful tool for studying
the behavior of complex systems and for solving a wide range of
mathematical problems.
5. Continuous State Space
• A system with a continuous state space is a system that can occupy
any point within a continuous range of states. For example, consider a
mass on a spring. The position of the mass can be any point along the
length of the spring, which forms a continuous range of possible
states for the system.
6. • In contrast, a system with a discrete state space can only occupy a
limited number of distinct states. For example, a two-state system,
such as a coin that can either be heads or tails, has a discrete state
space.
• The concept of a continuous state space is important in the study of
systems that can occupy a potentially infinite number of states, as it
allows for the use of techniques such as the matrix geometric method
to analyze their behavior.
7. Markov Chain
• A Markov chain is a mathematical system that undergoes transitions
from one state to another according to certain probabilistic rules. The
defining characteristic of a Markov chain is that no matter how the
system arrived at its current state, the possible future states are fixed.
In other words, the probability of transitioning to any particular state
is dependent solely on the current state and time elapsed.
8. • A Markov chain is often represented using a state transition diagram,
in which the states of the system are represented by nodes and the
transitions between states are represented by edges. The edges are
labeled with the probability of transitioning from one state to
another.
9. • Markov chains are used to model and analyze a wide variety of
systems, including systems in computer science, biology, economics,
and physics. They are particularly useful for analyzing systems that
exhibit memorylessness, which means that the probability of
transitioning to a new state depends only on the current state and
not on the sequence of states that preceded it.
10. Phase-Type Distribution
• A phase-type distribution is a probability distribution that can be
expressed as a mixture of exponential distributions, or phases. The
phase-type distribution is a generalization of the exponential
distribution, which is itself a special case of the phase-type
distribution.
11. • The phase-type distribution is often used to model the behavior of
systems that exhibit both continuous and discontinuous behavior,
such as systems with repairable components or systems that switch
between different modes of operation. The distribution can be
parameterized using a matrix, which specifies the probabilistic
transitions between the different phases of the distribution.
12. • The phase-type distribution has a number of useful properties,
including the ability to represent a wide range of shapes and the
ability to model systems with a countably infinite number of states. It
is often used in the analysis of Markov chains and other types of
stochastic systems.
13. How do you analyze a congested system using
Markov chain and matrix geometric analysis?
• Markov chains and matrix geometric methods can be used to analyze
the behavior of systems that exhibit "memoryless" properties,
meaning that the future state of the system depends only on its
current state and not on its past states. These techniques can be used
to analyze a congested system by modeling the system as a Markov
chain, where the states of the chain represent the different levels of
congestion that the system can be in, and the transitions between
states represent the movement of the system from one congestion
level to another.
14. • To analyze the system using matrix geometric methods, you would
first construct the transition matrix for the Markov chain, which
specifies the probabilities of transitioning between different states.
You can then use this matrix to calculate the stationary distribution of
the system, which represents the long-term behavior of the system,
as well as other important measures such as the expected time to
move between different states and the expected number of
transitions required to reach a particular state.
15. • It's also worth noting that Markov chain analysis can be used to
analyze other types of systems as well, not just congested systems.
For example, it has also been applied to fields such as economics,
biology, and computer science, to name a few.
16. Memoryless Properties
• In the context of Markov chains and matrix geometric analysis,
"memoryless" refers to the property of a system where the future
state of the system depends only on its current state, and not on its
past states. This means that, in a memoryless system, the probability
of transitioning to any particular future state is independent of the
sequence of states that the system has been in up to that point.
17. • For example, consider a system that represents the traffic on a busy
street. If we model this system as a Markov chain, the states of the
chain might represent different levels of congestion (e.g. low,
medium, high). In this case, the system exhibits memoryless
properties if the probability of transitioning from a low congestion
state to a high congestion state is independent of whether the system
was previously in a low congestion state or a medium congestion
state.
18. • Memoryless systems are often used to model real-world systems
because they are relatively simple to analyze and can capture many
important features of the system behavior. However, it's important to
keep in mind that not all systems are memoryless, and it may be
necessary to use more complex models to accurately represent the
behavior of certain systems.
19. Stationary Distribution
• The stationary distribution of a system represents the long-term
behavior of the system. It is a probability distribution over the states
of the system that describes the likelihood of the system being in
each state at a given time, assuming that the system has reached a
steady state (i.e. the distribution of states has become constant over
time).
20. • For example, consider a system that represents the traffic on a busy
street, where the states of the system represent different levels of
congestion (e.g. low, medium, high). If we construct a Markov chain
to model this system, the stationary distribution of the system would
describe the probability of the traffic being in a low congestion state,
a medium congestion state, or a high congestion state at any given
time, assuming that the traffic has reached a steady state (e.g. after a
long enough period of time).
21. • To calculate the stationary distribution of a system, you can use the
transition matrix of the system's Markov chain. The stationary
distribution is the unique probability distribution that satisfies the
equation:
stationary_distribution = stationary_distribution * transition_matrix
22. • In other words, the stationary distribution is the eigenvector of the
transition matrix with eigenvalue 1.
• The stationary distribution is an important measure in the analysis of
Markov chains because it describes the long-term behavior of the
system, which can be difficult to predict using other methods. It is
often used to answer questions such as: "What is the probability that
the system will be in a particular state at a given time?", or "How long
will it take for the system to reach a particular state?"
23. How do you analyze a congested system having
phase-type distribution with matrix geometric
method?
• To analyze a congested system using matrix geometric methods, you
can use a variant of the standard Markov chain model called a
"phase-type distribution" model. In this model, the states of the
system are represented by a set of phases, where each phase is
associated with a particular distribution over the states of the system.
The transitions between phases represent the movement of the
system from one congestion level to another.
24. • To analyze the system using matrix geometric methods, you would
first construct the transition matrix for the phase-type distribution
model, which specifies the probabilities of transitioning between
different phases. You can then use this matrix to calculate the
stationary distribution of the system, which represents the long-term
behavior of the system, as well as other important measures such as
the expected time to move between different phases and the
expected number of transitions required to reach a particular phase.
25. • It's worth noting that phase-type distribution models are a more
general and flexible way of modeling systems than standard Markov
chain models, since they allow for the representation of more
complex distributions over the states of the system. However, they
can also be more difficult to work with, since the calculations involved
are often more complex.