Uniform Sampling Algorithm

Input: Integer N >= 1
Output: R chosen uniformly at random from [0,N,-1]
Choose 1 to N Randomly (N)
1. Let T be the smallest power of 2 such that T >= N
2. compute R = RGB(log2(T))
3. if R < N then output R and halt
4. goto step(2)

Algorithm or Modeling of cell to cell transmission HIV-1

MODELING CELL-TO-CELL TRANSMISSION FOR HIV-1
Modes of Viral Transmission and Modeling Viral Dynamics
The well-known standard model of viral dynamics (reviewed in 27, 36)
represents the dominant and standard approach to analyze and quantify
the spread of a viral infection within a host. The model follows the
concentrations of target cells (T), infected cells (I), and virions (V).
Their interactions, depicted in Figure 1a, are mathematically 
described by the following system of ordinary differential equations:



1.equation 1
Target cells, T, which are cells susceptible to infection, are produced
at a constant rate λ and have an average lifetime of 1/dT. Infected 
cells, I, die with rate δ per cell and produce new virions at rate ρ 
that are cleared from the system at rate c per virion. In the formulation
given in Equation 1, infection of target cells is mediated (a) by 
cell-free virions at a rate dependent on the viral concentration, V, and
a transmission rate constant β and (b) by infected cells with a cell-to-cell
transmission rate constant ω. When cell-to-cell transmission is included
in the model, virus spread and target cell depletion are accelerated (Figure 1b).

Viewed on https://www.annualreviews.org/doi/full/10.1146/annurev-virology-110615-042249#_i24  19 March 2020

Log in vs Login

Log in and login have only seen heavy use since personal 
computers became ubiquitous in the 1980s, but they are 
now so common that misusing them in your writing can cost
you credibility. Log in (two words) should only be used 
as a verb. Login (one word) can be a noun or an adjective.

SORTING

            Writing Sorting Algorithm

Sorting it is the major part of computer routines with huge datasets
and loads of information to process these days, it is a good a idea
to understand of how of how works sort algorithms

Assuming we have an array of numbers like this:

   Unsorted Array my_Numbers = [20,5,16,19,9,15,2,18,17,8,12,1,3,7,10,8,6,11,4,13,14]


   Sorted Array my_Numbers = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]


We will look at the following sorting algorithms
   
            >> Selection sort
             >> Bubble sort
              >> Insertion sort
               >> Shell sort


   >>> Selection Sort    my_Numbers = [20,5,16,19,9,15,2,18,17,8,12,1,3,7,10,8,6,11,4,13,14]
       
       ALGORITHM
         

        
 var my_Numbers = [20,5,16,19,9,15,2,18,17,8,12,1,3,7,10,8,6,11,4,13,14];
        
 var temp;

        
 for(var i=0; i=my_Number.length; i++){
         
    for(var j=0; j=i+1; j++){ 
         
        if(my_Numbers[i] > my_Numbers[j]){
         
           temp = my_Numbers[j];
         
           my_Number[j] = temp;
        
         }
        
     }
       
 }
     


     

Karatsuba multiplication algorithm

The Karatsuba multiplication algorithm


The Karatsuba algorithm is  an efficient algorithm for multiplying two large numbers together.

It has a complexity of O(n^2) where n is the size in bits of the numbers being multiplied.

                                                               
    1.  Karatsuba(x,y)
    2.   if |x| <= 16 then return (x*y)
    3.       m =|x|/2
    4.       compute a and b such that x = a2^m+b
    5.       compute c and d such that y = c2^m+d
    6.       t = Karatsuba (a,c)
    7.       u = Karatsuba (a+b,c+d)
    8.       v = Karatsuba (a,d)
    9.  output (tv2^2m +(u-t-v)2^m +v) and halt


The reason that Karatsuba is faster than the classical approach is that it divides a problem 

into three problems of half the size.

Biological or Artificial Neural Networks

The ability to learn and to react to changes in our environment requires some

sort of energy or activity in this case our brain, with billion of network 

connections that interact each other in a glorious speed.


But is machine learning or artificial intelligence (AI) getting our jobs? at the 

moment humans has replicated the mathematical model of network for communication

still the proper algorithm and the hardware that can connect billion of connection

sort, learn, react, in a blink of an eye.

In the diagram you can see both  the biological and the artificial neural networks. 

The New Big Wave in Technology Machine Learning

Machine learning systems automatically learn programs from

data. This is often a very attractive alternative to manually

constructing them, and in the last decade the use of machine

learning has spread rapidly throughout computer science

and beyond.


Machine learning is used in Web search, spam

filters, recommender systems, ad placement, credit scoring,

fraud detection, stock trading, drug design, and many other

applications.

 LEARNING = REPRESENTATION + EVALUATION + OPTIMIZATION 






Algorithm 1 LearnDT(TrainSet)
  if all examples in TrainSet have the same class y∗ then
     return MakeLeaf(y∗)
  if no feature xj has InfoGain(xj ,y) > 0 then
     y∗ ← Most frequent class in TrainSet
     return MakeLeaf(y∗)
     x∗ ← argmaxxj
     InfoGain(xj ,y)
     TS0 ← Examples in TrainSet with x∗ = 0
     TS1 ← Examples in TrainSet with x∗ = 1
  return MakeNode(x∗, LearnDT(TS0), LearnDT(TS1))



Reference 2019/1/18 viewed url:https://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf

The Stable Marriage Algorithm

David Gale was born in Manhattan. During the years in which he was growing up

and attending school, his home was sometimes in New York City, sometimes in the surrounding 

district. He studied at Swarthmore College, Swarthmore, Pennsylvania, and was awarded a B.A. 

in mathematics in 1943. He then went to the University of Michigan to study for a Master's Degree

which he was awarded in 1947. For his doctoral research he went to Princeton where he undertook

research in game theory with Albert W Tucker as his thesis advisor. He was a Procter Fellow 

during 1948 and received a Ph.D. in 1949 for his thesis Solutions of Finite Two-Person Games.

Stable Marriage Algorithm


function stable Matching {
  	     Initialize all m ∈ M and w ∈ W to free
      while ∃ free man m who still has a woman w to propose to {
        w = first woman on m’s list to whom m has not yet proposed
       		 if w is free
           			        (m, w) become engaged
            else some pair (m', w) already exists
           if w prefers m to m'
         m' becomes free
       (m, w) become engaged 
    else
             (m', w) remain engaged
	      }
 }

Node.JS

Node.JS is a great platform to store internet radio shows as its asynchronous 

nature allows us to handle multiple streams at the same time without ever having to worry 

about different processes interfering with one another. This means we can  store different  

shows,  from different streams, to different locations at the same time.



              JSON
                {"name" : "Newsjack",
                 "radioStation" : "BBC Radio 4 Extra",
                 "playlistURL" : "http://www.bbc.co.uk/radio/listen/live/r4x_aacla.pls",
                 "startTime" : "22:30",
                 "duration"  : "25",
                 "recurs" : {
                 "every" : ["thursday"]
                }
             


You can see the JSON file has a description of the radio station as well the days

of the week that the show is on.

Reading our JSON file



Now that we have a JSON file describing our radio show, let's put it to use. 

Create an app.js file and require the following Node.JS modules



              var http: required('http'),
              fs = required('fs'),
              spaw = required('child_process).spawn;



getShowList  invoke that function to load in the JSON file.

The readFile function is an asynchronous method, so all data read will be passed

through to a callback.

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