This document discusses unification and anti-unification of terms. It provides an overview and basics of terms, equations, functions, variables, substitutions, and solutions. It describes the unification problem as taking an equation set as input and outputting an equivalent solved form. The document outlines Lassez's unification algorithm and provides an example. It then discusses the anti-unification problem as finding the least upper bound of terms in the complete lattice. An anti-unification algorithm is described using variable renaming and an example is provided.
It includes all the basics of calculus. It also includes all the formulas of derivatives and how to carry it out. It also includes function definition and different types of function along with relation.
It includes all the basics of calculus. It also includes all the formulas of derivatives and how to carry it out. It also includes function definition and different types of function along with relation.
En esta presentación se da una definición sencilla de lo que representa la derivada de una función y como se calcula utilizando su definición matemática
En esta presentación se da una definición sencilla de lo que representa la derivada de una función y como se calcula utilizando su definición matemática
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Determine whether a function is even, odd, or neither from its graph.
* Graph functions using compressions and stretches.
* Combine transformations.
This pdf is about the Schizophrenia.
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(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
5. UNIFICATION PROBLEM
¡ Input: equation E
¡ Output: E equivalent Solved form equation set
¡ equation
¡ Solved form: equation variable variable
equation
¡ equivalent: solution
g(x) = g(g(z))
f(a, z) = f(a, y)
x = g(y)
z = y
Problem E Solved Form
equivalent
6. UNIFICATION ALGORITHM [LASSEZ ET AL.]
Input: equation set E
E equation
s, t , x variable, f, g function symbol
1. f(t1, ..., tn) = f(s1, ..., sn)
→ t1=s1, ..., tn=sn
2. f(t1, ..., tn) = g(s1, ..., sm) f ≠g
→
3. x = x
→ equation
( )
7. UNIFICATION ALGORITHM [LASSEZ ET AL.]
4. t = x t variable
→ x = t
5. x = t t x equation x
i. x t
→
ii. x t
→ equation x t
8. EXAMPLE
g(x) = g(g(z))
f(a, z) = f(a, y)
x = g(z)
f(a, z) = f(a, y)
1
x = g(z)
a = a
z = y
1
1x = g(z)
z = y
5.ii
x = g(y)
z = y
9. 1. f(t1, ..., tn) = f(s1, ..., sn)
→ t1=s1, ..., tn=sn
2. f(t1, ..., tn) = g(s1, ..., sm) f ≠g
→
3. x = x
→ equation
4. t = x t variable
→ x = t
f
equation
10. 5. x = t t x equation
x
i. x t
→
ii. x t
→ equation x t
variable function symbol
1 variable 1
13. ANTI-UNIFICATION PROBLEM
¡ θ = { v1 -> t1, ..., vn -> tn }
¡ tθ t vi ti term
¡ t s instance ⇔ s t anti-instance ⇔ s ≧ t
⇔ inst(s) ⊇ inst(t) ⇔ θ t = sθ
¡ inst(t): t instance
¡ variable renaming
≧ complete lattice (inst(⊥)=∅ ⊥ )
¡ ex. f(x, y) f(y, z)
¡ lattice least upper bound anti-unification
complete lattice
poset subset
greatest lower bound least
upper bound
14. EXAMPLE
f(a, g(a, y), a)
f(x, g(x, y), a)
f(x, g(x, b), a)
f(b, g(b, b), a)
x=a y=b
x=b
f(x, g(x, x), a)
y=x
x=b
anti-unification
f(x, g(x, x), y)
y=a
f(x, g(x, y), x)
x=a
... ...
...
15. ANTI-UNIFICATION ALGORITHM
¡ φ: T × T -> V': bijection term variable
¡ T: term , V': variable
¡ λ: Anti-unification
¡ λ( f(s1, ..., sm), f(t1, ..., tm) ) = f( λ(s1, t1), ..., λ(sm, tm) )
¡ λ( s, t ) = φ( s, t )
16. EXAMPLE
λ( f(a, g(a, y), a), f(b, g(b, b), a) )
= f( λ(a, b), λ(g(a, y), g(b, b)), g(a, a) )
= f( x, g( λ(a, b), λ(y, b) ), a )
= f( x, g( x, y ), a )
φ(a, b) = x
φ(y, b) = y
