Formulas usadas para el análisis de algoritmos.
Se muestra una serie de propiedades de logaritmos, combinatoria, formulas de sumatoria, reglas de sumatorias, fórmulas para pisos y cielos, aproximación de sumatorias mediante integrales definidas.
Ejercicios resueltos de Identidad ángulo medio usando seno y coseno para la solución de los mismos. Trigonometría
Mayor información: https://www.matematicabasica.com
Ejercicios resueltos de Identidad ángulo medio usando seno y coseno para la solución de los mismos. Trigonometría
Mayor información: https://www.matematicabasica.com
Lenguaje Algebraico, es la expresión literal y simbólica de las operaciones algebraicas, que desarrollan el pensamiento funcional, como la forma de analizar los elementos aritméticos que conforman las expresiones matemáticas.
Las expresiones algebraicas son combinaciones de números y letras unidos por las operaciones fundamentales del álgebra, dando como resultado monomios y polinomios.
El presente documento recopila la comprensión de estos conceptos y sus procesos matemáticos mediante el desarrollo de ejercicios que así lo evidencian.
Lenguaje Algebraico, es la expresión literal y simbólica de las operaciones algebraicas, que desarrollan el pensamiento funcional, como la forma de analizar los elementos aritméticos que conforman las expresiones matemáticas.
Las expresiones algebraicas son combinaciones de números y letras unidos por las operaciones fundamentales del álgebra, dando como resultado monomios y polinomios.
El presente documento recopila la comprensión de estos conceptos y sus procesos matemáticos mediante el desarrollo de ejercicios que así lo evidencian.
A Mathematically Derived Number of Resamplings for Noisy Optimization (GECCO2...Jialin LIU
"A Mathematically Derived Number of Resamplings for Noisy Optimization". Jialin Liu, David L. St-Pierre and Olivier Teytaud. (Accepted as short paper) Genetic and Evolutionary Computation Conference (GECCO), 2014.
Using serpentine matrices and reflections on their columns of even order we present a computer program that generates a large class of semi-magic squares and magic squares.
What is an Algorithm
Time Complexity
Space Complexity
Asymptotic Notations
Recursive Analysis
Selection Sort
Insertion Sort
Recurrences
Substitution Method
Master Tree Method
Recursion Tree Method
Objetos gráficos (line, text, patch, surface, light, image).
Gráficos específicos (para presentaciones, probabilidad y estadística, para sistemas lineales, funciones de teoría de sistemas).
Animaciones.
Documento con información acerca de cómo sacarle lo mejor a nuestra cámara fotográfica.
Conceptos básicos de fotografía (modo manual, ley de reciprocidad, bracketing, panorámicas).
Descripción de los conceptos para las sumatorias usadas en el análisis de algoritmos.
Se presenta la notación, sumatorias y recurrencias, manipulación de sumatorias, múltiplas sumatorias, métodos generales, cálculo mediante límites y finalmente una lista de ejercicios.
Primera versión del manual de análisis y diseño de algoritmos por parte del área de informática de la INACAP.
Manual interesante para el análisis y diseño de algoritmos.
Créditos a Víctor Valenzuela.
Capítulo 1.
Se muestra que el factor predominante que delimita lo que es soluble en un tiempo razonable de lo que no lo es.
Se muestran los conceptos sobre asíntotas.
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.
(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.
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.
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.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
The increased availability of biomedical data, particularly in the public domain, offers the opportunity to better understand human health and to develop effective therapeutics for a wide range of unmet medical needs. However, data scientists remain stymied by the fact that data remain hard to find and to productively reuse because data and their metadata i) are wholly inaccessible, ii) are in non-standard or incompatible representations, iii) do not conform to community standards, and iv) have unclear or highly restricted terms and conditions that preclude legitimate reuse. These limitations require a rethink on data can be made machine and AI-ready - the key motivation behind the FAIR Guiding Principles. Concurrently, while recent efforts have explored the use of deep learning to fuse disparate data into predictive models for a wide range of biomedical applications, these models often fail even when the correct answer is already known, and fail to explain individual predictions in terms that data scientists can appreciate. These limitations suggest that new methods to produce practical artificial intelligence are still needed.
In this talk, I will discuss our work in (1) building an integrative knowledge infrastructure to prepare FAIR and "AI-ready" data and services along with (2) neurosymbolic AI methods to improve the quality of predictions and to generate plausible explanations. Attention is given to standards, platforms, and methods to wrangle knowledge into simple, but effective semantic and latent representations, and to make these available into standards-compliant and discoverable interfaces that can be used in model building, validation, and explanation. Our work, and those of others in the field, creates a baseline for building trustworthy and easy to deploy AI models in biomedicine.
Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
1. APPENDIX A
Useful Formulas for the
Analysis of Algorithms
This appendix contains a list of useful formulas and rules that are helpful in the
mathematical analysis of algorithms. More advanced material can be found in
[Gra94], [Gre07], [Pur04], and [Sed96].
Properties of Logarithms
All logarithm bases are assumed to be greater than 1 in the formulas below; lg x
denotes the logarithm base 2, ln x denotes the logarithm base e = 2.71828 . . . ;
x, y are arbitrary positive numbers.
1. loga 1 = 0
2. loga a = 1
3. loga xy = y loga x
4. loga xy = loga x + loga y
5. loga
x
y
= loga x − loga y
6. alogb x = xlogb a
7. loga x =
logb x
logb a
= loga b logb x
Combinatorics
1. Number of permutations of an n-element set: P(n) = n!
2. Number of k-combinations of an n-element set: C(n, k) = n!
k!(n − k)!
3. Number of subsets of an n-element set: 2n
475
2. 476 Useful Formulas for the Analysis of Algorithms
Important Summation Formulas
1.
u
i=l
1 = 1 + 1 + . . . + 1
u−l+1 times
= u − l + 1 (l, u are integer limits, l ≤ u);
n
i=1
1 = n
2.
n
i=1
i = 1 + 2 + . . . + n =
n(n + 1)
2
≈
1
2
n2
3.
n
i=1
i2
= 12
+ 22
+ . . . + n2
=
n(n + 1)(2n + 1)
6
≈
1
3
n3
4.
n
i=1
ik
= 1k
+ 2k
+ . . . + nk
≈
1
k + 1
nk+1
5.
n
i=0
ai
= 1 + a + . . . + an
=
an+1
− 1
a − 1
(a = 1);
n
i=0
2i
= 2n+1
− 1
6.
n
i=1
i2i
= 1 . 2 + 2 . 22
+ . . . + n2n
= (n − 1)2n+1
+ 2
7.
n
i=1
1
i
= 1 +
1
2
+ . . . +
1
n
≈ ln n + γ , where γ ≈ 0.5772 . . . (Euler’s constant)
8.
n
i=1
lg i ≈ n lg n
Sum Manipulation Rules
1.
u
i=l
cai = c
u
i=l
ai
2.
u
i=l
(ai ± bi) =
u
i=l
ai ±
u
i=l
bi
3.
u
i=l
ai =
m
i=l
ai +
u
i=m+1
ai, where l ≤ m < u
4.
u
i=l
(ai − ai−1) = au − al−1
3. Useful Formulas for the Analysis of Algorithms 477
Approximation of a Sum by a Definite Integral
u
l−1
f (x)dx ≤
u
i=l
f (i) ≤
u+1
l
f (x)dx for a nondecreasing f (x)
u+1
l
f (x)dx ≤
u
i=l
f (i) ≤
u
l−1
f (x)dx for a nonincreasing f (x)
Floor and Ceiling Formulas
The floor of a real number x, denoted x , is defined as the greatest integer not
larger than x (e.g., 3.8 = 3, −3.8 = −4, 3 = 3). The ceiling of a real number x,
denoted x , is defined as the smallest integer not smaller than x (e.g., 3.8 = 4,
−3.8 = −3, 3 = 3).
1. x − 1 < x ≤ x ≤ x < x + 1
2. x + n = x + n and x + n = x + n for real x and integer n
3. n/2 + n/2 = n
4. lg(n + 1) = lg n + 1
Miscellaneous
1. n!≈
√
2πn
n
e
n
as n → ∞ (Stirling’s formula)
2. Modular arithmetic (n, m are integers, p is a positive integer)
(n + m) mod p = (n mod p + m mod p) mod p
(nm) mod p = ((n mod p)(m mod p)) mod p