This document contains lecture slides on nonlinear programming from lectures given at MIT. It discusses two main issues in nonlinear programming: 1) characterizing solutions through necessary and sufficient conditions using concepts like Lagrange multipliers and sensitivity analysis, and 2) computational methods for finding solutions through iterative algorithms. It provides examples of application areas for nonlinear programming like data networks, production planning, and engineering design. It outlines topics covered in the first lecture, including duality theory and the relationship between linear and nonlinear programming.
This presentation is trying to explain the Linear Programming in operations research. There is a software called "Gipels" available on the internet which easily solves the LPP Problems along with the transportation problems. This presentation is co-developed with Sankeerth P & Aakansha Bajpai.
By:-
Aniruddh Tiwari
Linkedin :- http://in.linkedin.com/in/aniruddhtiwari
Linear programming
Application Of Linear Programming
Advantages Of L.P.
Limitation Of L.P.
Slack variables
Surplus variables
Artificial variables
Duality
Jacobi Iteration Method is Used in Numerical Analysis. This slide helps you to figure out the use of the Jacobi Iteration Method to submit your presentatio9n slide for academic use.
This presentation is trying to explain the Linear Programming in operations research. There is a software called "Gipels" available on the internet which easily solves the LPP Problems along with the transportation problems. This presentation is co-developed with Sankeerth P & Aakansha Bajpai.
By:-
Aniruddh Tiwari
Linkedin :- http://in.linkedin.com/in/aniruddhtiwari
Linear programming
Application Of Linear Programming
Advantages Of L.P.
Limitation Of L.P.
Slack variables
Surplus variables
Artificial variables
Duality
Jacobi Iteration Method is Used in Numerical Analysis. This slide helps you to figure out the use of the Jacobi Iteration Method to submit your presentatio9n slide for academic use.
Machine Learning Foundations for Professional ManagersAlbert Y. C. Chen
20180526@Taiwan AI Academy, Professional Managers Class.
Covering important concepts of classical machine learning, in preparation for deep learning topics to follow. Topics include regression (linear, polynomial, gaussian and sigmoid basis functions), dimension reduction (PCA, LDA, ISOMAP), clustering (K-means, GMM, Mean-Shift, DBSCAN, Spectral Clustering), classification (Naive Bayes, Logistic Regression, SVM, kNN, Decision Tree, Classifier Ensembles, Bagging, Boosting, Adaboost) and Semi-Supervised learning techniques. Emphasis on sampling, probability, curse of dimensionality, decision theory and classifier generalizability.
https://telecombcn-dl.github.io/2017-dlai/
Deep learning technologies are at the core of the current revolution in artificial intelligence for multimedia data analysis. The convergence of large-scale annotated datasets and affordable GPU hardware has allowed the training of neural networks for data analysis tasks which were previously addressed with hand-crafted features. Architectures such as convolutional neural networks, recurrent neural networks or Q-nets for reinforcement learning have shaped a brand new scenario in signal processing. This course will cover the basic principles of deep learning from both an algorithmic and computational perspectives.
Supervised learning is a machine learning paradigm where the algorithm is trained on a labeled dataset, learning patterns and relationships between input features and corresponding output labels to make accurate predictions on new, unseen data. It involves a teacher-supervisor relationship, where the algorithm strives to minimize the error between its predictions and the actual outcomes during training.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
1. LECTURE SLIDES ON NONLINEAR PROGRAMMING
BASED ON LECTURES GIVEN AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MASS
DIMITRI P. BERTSEKAS
These lecture slides are based on the book:
“Nonlinear Programming,” Athena Scientific,
by Dimitri P. Bertsekas; see
http://www.athenasc.com/nonlinbook.html
The slides are copyrighted but may be freely
reproduced and distributed for any noncom-
mercial purpose.
3. NONLINEAR PROGRAMMING
min f(x),
x∈X
where
• f : n → is a continuous (and usually differ-
entiable) function of n variables
• X = n or X is a subset of n with a “continu-
ous” character.
• If X = n, the problem is called unconstrained
• If f is linear and X is polyhedral, the problem
is a linear programming problem. Otherwise it is
a nonlinear programming problem
• Linear and nonlinear programming have tradi-
tionally been treated separately. Their method-
ologies have gradually come closer.
4. TWO MAIN ISSUES•
• Characterization of minima
− Necessary conditions
− Sufficient conditions
− Lagrange multiplier theory
− Sensitivity
− Duality
• Computation by iterative algorithms
− Iterative descent
− Approximation methods
− Dual and primal-dual methods
5. APPLICATIONS OF NONLINEAR PROGRAMMING•
• Data networks – Routing
• Production planning
• Resource allocation
• Computer-aided design
• Solution of equilibrium models
• Data analysis and least squares formulations
• Modeling human or organizational behavior
6. CHARACTERIZATION PROBLEM
• Unconstrained problems
− Zero 1st order variation along all directions
• Constrained problems
− Nonnegative 1st order variation along all fea-
sible directions
• Equality constraints
− Zero 1st order variation along all directions
on the constraint surface
− Lagrange multiplier theory
• Sensitivity
7. COMPUTATION PROBLEM
• Iterative descent
• Approximation
• Role of convergence analysis
• Role of rate of convergence analysis
• Using an existing package to solve a nonlinear
programming problem
9. DUALITY
• Min-common point problem / max-intercept prob-
lem duality
0 0
Min Common Point
Max Intercept Point Max Intercept Point
Min Common Point
S S
(a) (b)
Illustration of the optimal values of the min common point
and max intercept point problems. In (a), the two optimal
values are not equal. In (b), the set S, when “extended
upwards” along the nth axis, yields the set
S¯ = {¯ xn ≥ xn, ¯x | for some x ∈ S, ¯ xi = xi, i = 1, . . . , n − 1}
which is convex. As a result, the two optimal values are
equal. This fact, when suitably formalized, is the basis for
some of the most important duality results.
