Linear Algebra – Bernoulli Random Matrix At least one column is zero

Accept $ M_n $ is a $ n times n $ Matrix with independent entries $$ M_n (i, j) $$ Be $ 0.1 $ Bernoulli random variables, each with $$ mathbb {P} (M_n (i, j) = 1) = dfrac { ln n} {n} $$

How do we show that as $ n to infty $the probability that at least one column is zero is delimited $ 0 $ (ie with a positive probability)?

We can use the inclusion and exclusion principle to obtain a series and use mathematica as the first term in the series $$ n (1- dfrac { ln n} {n}) ^ n to 1 $$ We can probably use the alternate series test to draw the conclusion. However, it is difficult for me to calculate the above limit (and the limit of the other terms in the series) by hand.

Every help is appreciated.

Sharepoint Internal names of the person or group column are changed when the list template is added

I have created a person or group column in the list. If I take a list template and use it on another site, the internal name of the person or group column is changed. I have used the internal names of this column in my code. Because of this internal name mismatch, the code fails.

sharepoint online – creates a calculated column with the value yes IF ([due date]=[Today]-31, "Yes", No) or custom view

I'm trying to set up a calculated column to show a different calculated date column, and if it's less than a month (that is, need to be refreshed), say "yes."

If I can not, can I then create a custom view from a calculated date column?

The value greater than or equal to (today) -31 does not work for calculated columns?

My ultimate goal is to use Flow to look for the Yes column and then create a new list item, but I can not use Odata filters from calculated columns and (Today) -31 does not work for calculated columns? A bit stuck

sql – Converts each column value to a column name

I think my question is very simple and the answer must be simple too. I just want something like a pivot in one of my three columns.
I have a question like this:

SELECT AgentId, ReferenceTitle, PaymentValue FROM AgentPayments WHERE PaymentValue > 0

The result will look something like this:

AgentId       ReferenceTitle      PaymentValue     
AgentId1      ReferenceTitle1     PayementValue1  
AgentId1      ReferenceTitle2     PayementValue2   
AgentId1      ReferenceTitle3     PayementValue3
AgentId2      ReferenceTitle2     PayementValue4
AgentId3      ReferenceTitle2     PayementValue5
AgentId3      ReferenceTitle3     PayementValue6    

As you can see, there are some records back for me. Now I want to convert the result so that each value of the column & # 39; ReferenceTitle & # 39; as follows becomes a separate column:

AgentId     ReferenceTitle1      ReferenceTitle2     ReferenceTitle3            
AgentId1     PayementValue1      PayementValue2       PayementValue3
AgentId2         NULL            PayementValue4            NULL
AgentId3         NULL            PayementValue5       PayementValue6

I've just found very complicated search results, but I think there must be a simple solution.
do you think like me

Easy way to add "Link to Element" to any column in the SharePoint Online List set to "Modern Experience"

Stack Exchange network

The Stack Exchange network consists of 175 Q & A communities, including Stack Overflow, the largest and most trusted online community where developers can learn, share, and build a career.

Visit Stack Exchange

mysql – Groups by value and returns results in a generated column

I'm trying to figure out how to do it, but I have no idea how to do it.

I have a table (below) that has object_id's, types, and values. The values ​​are always unique and the type is always Type1, Type2 or Type3.

id   object_id   type    value
1    1           type1   123
2    1           type2   456
3    2           type3   789

The bottom line I'm trying to get is to consolidate all object_ids and return the types associated with "virtual columns" that are Type1, Type2, and Type3.

object_id   type1  type2  type3
   1        123    456    null
   2        null   null   789

I am not sure if this is possible in mySql or if I should just try it in PHP. Any help would be appreciated

Calculated column – The conditional syntax can not be displayed correctly

Have (animal) column with selection values ​​of 0,1,2,3.

If (Tier) = 0 calculated column should = 0
If (Tier) = 1 calculated column should = 4
If (Tier) = 2 calculated column should = 24
If (Tier) = 3 calculated column should = 48

Can work with 2 values ​​for the following syntax, but not 4 values:


linear algebra – the inverse of the sum of an identity and a Kronecker product after adding a column or removing a row

To let $ Q = alpha mathbb {I} + (S otimes S) ^ T (S otimes S) = alpha mathbb {I} + S ^ TS otimes S ^ TS $, Where $ mathbb {I} $ is $ n ^ 2 times n ^ 2 $ Matrix, $ S $ is a $ m times n $ binary matrix and $ otimes $ is a Kronecker product. I have some questions:

First, if we can write $ S ^ TS = sum_ {i = 1} ^ m s_i ^ Ts_i $ With what could we use the first-rate update properties, what would the update come from? $ Q ^ {- 1} $if we remove that $ i $-th row of $ S $? Can we extend the Sherman-Morrison formula for this case? For example, if we have $ M = ( alpha mathbb {I} + S ^ TS) ^ {- 1} $ then the updated inverse after removing the $ i $-th row would be
$$ M _ {- i} = M frac {Ms_i ^ Ts_i M} {s_iMs_i ^ T-1} $$

Second, what about adding a column to the matrix? $ S $How about the opposite of $ Q $ Change? Can we again use similar properties of the partitioned matrix?

Is there a way to compare a column value of the next row with the current row in a Dataset object in Spark using Java?

I am trying to convert an existing dataset to the new schema using the scheme below using Java

current scheme

id roll_no student
1 1232 John
2 1456 anna
3 1832 mike
4 2002 Dave

should turn into a new schema based on roll_no and add next_student if roll_no is next to the current student

id roll_no student next_student
1 1232 John Mike
2 1234 anna dave
3 1233 mike anna
4 1235 Dave zero

Is there a way to compare the column value of different rows in the dataset to do this. I would appreciate any hints to solve this problem.

Scala and PySpark display Window Object Lag and Lead methods, but I want to know if there's a way in Java

How can I "cancel" a cell from a column to get the correct average?

Google Pages. I need to set up my page for 20 rows of data in a Google spreadsheet (please understand). Often I only have to enter about 15 lines of data. Sheets will average at the bottom of each column based on all 20 cells (taking empty cells into account as zero). If I have an empty cell, how do I remove it from the average?