1) Divide and conquer algorithms break down a problem into smaller subproblems, solve those subproblems recursively, and then combine the results.
2) Merge sort is a classic example - it divides an array in half, recursively sorts each half, and then merges the sorted halves together. This takes O(n log n) time.
3) Common divide and conquer recurrences include T(n) = 2T(n/2) + O(n) which yields O(n log n) time, and T(n) = T(n-1) + O(1) which is O(n) time. Being able to recognize these recurrences can help analyze algorithm run times.
In ancient cultures the favorite question of sishya to his guru was "Who Am I?" and in the end he learnt everything about Reality. If you want a similar question in mathematics, ask "Is Riemann Hypothesis true?", and you will learn almost everything about mathematics. This presentation gives an elementary introduction to zeta functions using natural functions.
Sorting
Performance parameters
Insertion Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Shell Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
In ancient cultures the favorite question of sishya to his guru was "Who Am I?" and in the end he learnt everything about Reality. If you want a similar question in mathematics, ask "Is Riemann Hypothesis true?", and you will learn almost everything about mathematics. This presentation gives an elementary introduction to zeta functions using natural functions.
Sorting
Performance parameters
Insertion Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Shell Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Database structure Structures Link list and trees and Recurison complete Adnan abid
Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete
Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete
I am Gill K. I am an Operating System Assignment Expert at programminghomeworkhelp.com. I hold a PhD. in Programming at Manchester University, UK. I have been helping students with their homework for the past 6 years. I solve assignments related to Operating System Assignment.
Visit programminghomeworkhelp.com or email support@programminghomeworkhelp.com.
You can also call on +1 678 648 4277 for any assistance with Operating System Assignment.
Abstract:
This paper deals with the vital role of primitive polynomials for designing PN sequence generators. The standard LFSR (linear feedback shift register) used for pattern generation may give repetitive patterns. Which are in certain cases is not efficient for complete test coverage. The programmable LFSR based on primitive polynomial generates maximum-length PRPG with maximum fault coverage.
In this presentation, I have discussed what divide and conquer is, its advantages, disadvantages and its applications like merge sort, binary search etc.
Database structure Structures Link list and trees and Recurison complete Adnan abid
Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete
Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete
I am Gill K. I am an Operating System Assignment Expert at programminghomeworkhelp.com. I hold a PhD. in Programming at Manchester University, UK. I have been helping students with their homework for the past 6 years. I solve assignments related to Operating System Assignment.
Visit programminghomeworkhelp.com or email support@programminghomeworkhelp.com.
You can also call on +1 678 648 4277 for any assistance with Operating System Assignment.
Abstract:
This paper deals with the vital role of primitive polynomials for designing PN sequence generators. The standard LFSR (linear feedback shift register) used for pattern generation may give repetitive patterns. Which are in certain cases is not efficient for complete test coverage. The programmable LFSR based on primitive polynomial generates maximum-length PRPG with maximum fault coverage.
In this presentation, I have discussed what divide and conquer is, its advantages, disadvantages and its applications like merge sort, binary search etc.
Basic Computer Engineering Unit II as per RGPV SyllabusNANDINI SHARMA
Algorithm, Flowchart, Categories of Programming Languages, OOPs vs POP, concepts of OOPs, Inheritance, C++ Programming, How to write C++ program as a beginner, Array, Structure, etc
Recursion is a technique in programming where a function calls itself to solve smaller instances of the same problem. It involves two main components: the base case and the recursive case. The base case is the condition that stops the recursive calls, preventing infinite loops. The recursive case is where the function continues to call itself, breaking the problem down into smaller parts. For example, calculating the factorial of a number can be done using recursion, where `n! = n * (n-1)!` with `0! = 1` as the base case.
In data structures, recursion is commonly used for tasks like traversing or searching through trees and linked lists. It simplifies complex problems by dividing them into more manageable subproblems. For instance, in binary trees, recursive methods are used for traversals such as Preorder, Inorder, and Postorder, which visit nodes in a specific order using recursive function calls.
Here is the first set of notes for the first class in Analysis of Algorithm. I added a dedicatory for my dear Fabi... she has showed me what real idealism is....
This slide deck goes over the concept of recurrence relations and uses that to build-up to the concept of the Big O notation in computer science, math, and asymptotic analysis of algorithms.
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.
Richard's entangled aventures in wonderlandRichard 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.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
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.
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.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
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.
1. Chapter 9
Divide and Conquer
Divide and conquer: the
algorithmic version of recursion
Divide and conquer is closely related to recursion—you could even say that it is
nothing more. It has the same structure as recursion. We often implement divide
and conquer algorithms in terms of recursive functions, but we do not need to. The
defining characteristic of these algorithms is that we reduce a problem to smaller
versions of the same problem
Example: Merge sort
For example, if we want to sort a sequence, then we can split it into two sub-
sequences that we sort and then we can merge the two. The step where we sort
the two sub-sequences is the recursive step. It might feel circular to sort in terms
of sorting, but we are saved from circularity by base cases in the recursion.
2. The merge sort algorithm works like this:
1) Split the input in two
2) Sort the two halves
3) Combine then by merging them
Since we cut the input in half every time we call for a recursive solution, we never
get more than O(log n) function calls deep. Since the number of calls at each level
grows by powers of two as the size of the problems shrink by powers of two, we
end up with a running time of O(n log n).
Notice that this is faster than the other sorting algorithms we have seen. It is
optimal in the sense that no comparison-based sorting algorithms can run faster
than O(n log n).
Examples
Some are just a rephrasing of
algorithms you have already seen…
Divide and conquer is a powerful approach to designing new algorithms, but we
can also rephrase some we have already seen as divide and conquer.
3. DnC formulation of linear search:
1) Check the first element in our sequence and report if it matches
2) Do a linear sort on the rest of the sequence
Selection sort:
1) move the smallest element to the first location in the sequence,
2) sort the rest of the sequence
The "first location in the sequence" is the first location in the sequence we consider
in the recursion. Not the full sequence.
Binary search:
1) check the middle element. Report it found if it is a match.
2) Do a binary search in the left or right half
4. Sum (less likely to lose significant bits):
1) Compute the sum of both halves of the input
2) Add the sums together
Sum (less likely to lose significant bits):
1) Add all pairs of the input
2) Compute the sum of these
Common running times
Honestly, I find it easier just to memorise
these than redo the math each time…
They keep popping up…
There are a few recurrence equations that show up a lot for divide and conquer
running times. There are some general techniques when the recurrence doesn’t
match this but sometimes you just have to work out the math. If you can recognise
one of these recurrences for your algorithm, then just use these equations.
5. We have already seen why T(n) = O(1) + 2T(n/2) is in O(n log n)
It isn’t hard to see that T(n) = T(n - 1) + O(1) must be O(n) either. The argument is
not different from the one we had for the running time of linear search.
For selection sort we can argue that we recurse to depth n and at each level we
perform a search that costs O(n). The running time must then be O(n²) — as we
also argued first time we saw selection sort.
6. Binary search was already a divide and conquer algorithm (although we didn’t
implement it using recursion). We now it can reach call depth O(log n) but it only
does constant time at each level.
It might be less obvious what the running time of T(n) = 2T(n/2) + O(1) is, but we
can argue as follows
1) We cut the problem size in half each time we solve a recursive problem,
therefore we go to call depth log n
2) We double the number of operations we must do at each level
3) You have to know this sum, but it is easy (see next slide)
This sketch doesn’t give us the exact sum, but we can see that if we double the
number we add at each step up to n, then the sum is less than 2n
7. We can also consider summing in the other direct, starting with n. If we half the
number each time we add a new one, then regardless of where we stop, we will
have a sum that is less than 2n.
In this algorithm we spend linear time per level and cut the problem size in two
when going from one level to the next. The sum is the same as before (more or
less) and we have a linear time algorithm.
Exercises!
Time to put divide-and-
conquer into practice