I have a Bernoulli equation (attached below). So this is need to be converted to ODE. I tried to solve it by a separation of variables but I could not. Can anyone help me with the code for this, please?

# Tag: case

## Collecting consumer contact information to alert individuals in case of data breach for B2B companies

If you are a B2B company [US], you may collect data on your clients as well as your clients’ customers. For example, let’s say the only thing you need to collect is your clients’ customers’ names.

In the case that your company has a data leak and the individuals’ names are shared with an unauthorized third party, (I believe) you have an obligation to inform *someone*.

What is the standard practice? Do you directly email the individual and say their information was leaked? Or do you give your client (a business) a list of the client’s whose data was impacted and let them reach out to the impacted clients.

In the case of emailing the impacted clients directly, what if you do not collect their contact information, and have no way to contact them?

Real world example: my personal data was leaked by a B2B software company that I had never heard of. I was contacted by the software company directly as well as their client who I had used the services of. Was it the responsibility of the B2B software company to collect my email in case they needed to contact me directly?

## Are hardware security keys (e.g ones supporting Fido2) “able to protect authentication” even in case of compromised devices?

Correct me if I am wrong, please.

I understand that 2FA (MFA) increases account security in case an attacker obtains a password which might be possible via various ways, e.g. phishing, database breach, brute-force, etc..

However, if the 2FA device is compromised (full system control) which can also be the very same device then 2FA is broken. It’s not as likely as opposed to only using a password but conceptually this is true.

Do hardware security keys protect against compromised devices? I read that the private key cannot be extracted from those devices. I think about protecting my ssh logins with a FIDO2 key. Taking ssh as an example, I would imagine that on a compromised device the ssh handshake and key exchange can be intercepted and the Fido2 key can be used for malicious things.

Additionally: Fido2 protects against phishing by storing the website it is setup to authenticate with. Does FIDO2 and openssh also additionally implement host key verification or doesn’t it matter because FIDO2 with openssh is already asymmetric encryption and thus not vulnerable to MitM attacks?

## Finding the worst case running time of this piece of code?

I am working with this code:

`function strange (list a[0..n-1] of integers such that abs(a[i]) ≤ n for every 0 ≤ i ≤ n - 1, list b[0..2n] of zeroes) for i ← 0 to n - 1 do a[i] ← a[i] + n for i ← 0 to n - 1 do for j ← 0 to abs(a[i] - 1) do b[j] ← b[j] + 1 return b `

I am trying to figure out the worst running time for the code above and so far I’m guessing that the first for loop will run n times, but not sure how to prove this. For the second and third for loop, I’m unsure how to approach this. If possible, could someone help me solve this?

## Difficulty understanding the use of arbitrary function for the worst case running time of an algorithm

In CLRS the author said

"Technically, it is an abuse to say that the running time of insertion sort is $ O(n^2)$ , since for a given $ n$ , the actual running time varies, depending on the particular input of size $ n$ . When we say “the running time is $ O(n^2)$ ,” we mean that there is a function $ f(n)$ that is $ O(n^2)$ such that for any value of $ n$ , no matter what particular input of size $ n$ is chosen, the running time on that input is bounded from above by the value $ f(n)$ . Equivalently, we mean that the worst-case running time is $ O(n^2)$ . "

What I have difficulties understanding is why did the author talked about an arbitrary function $ f(n)$ instead of directly $ n^2$ .

I mean why didn’t the author wrote

"When we say “the running time is $ O(n^2)$ ,” we mean that for any value of $ n$ , no matter what particular input of size $ n$ is chosen, the running time on that input is bounded from above by the value $ cn^2$ for some +ve $ c$ and sufficiently large n. Equivalently, we mean that the worst-case running time is $ O(n^2)$ ".

I have very limited understanding of this subject so please forgive me if my question is too basic.

## SQL: CASE WHEN having AVG() as condition not giving right output

I have a table of unique users that each has a "rating" column (it’s an average rating they give out of all their ratings given in a different table of reviews). I want to add another column to my table, which specifies either them giving a rating that is above the average of all ratings of all users (hence I use the AVG() function), below or at average (I call it "bias"). In other words, I want to see whether each user gives on average higher or lower ratings than the total average. I understand the limitedness of this query, and ideally I would include an interval (i.e. within 0.5 points below or above average still counts as average) but I can’t seem to make even the simplest query work.

I’ve been using the Yelp dataset from a Coursera course, but I tried to create a sample that produces the same result that I do not want – *just one row*. I want to have this categorization for each row, hence it should return 3 rows in this example, "below average" in the first two and "above average" in the third. However, the code below produces just one row. I have been working with R and this seems like I am using incorrect syntax, but after 30 minutes of searching the web I cannot find a solution.

**I am working in and want to use SQLite syntax as part of the course in Coursera**

`CREATE TABLE test ( id integer primary key, rating integer ); INSERT INTO test (id, rating) VALUES (1, 1); INSERT INTO test (id, rating) VALUES (2, 3); INSERT INTO test (id, rating) VALUES (3, 8); SELECT id, rating, CASE WHEN rating > AVG(rating) THEN "above average" WHEN rating < AVG(rating) THEN "below average" ELSE "no bias" END AS "bias" FROM test `

## Open Source SIEM Case Management [closed]

I’m wondering if there are any open source SIEM case management platforms **(e.g. the case management in Logrhythm SIEM)?**

I need to integrate my SIEM with case management; so I can link the alarms with cases.

## Recording a histogram in a tree exhibits strange best case

The task is to record a histogram from a streaming data source.

One data point is, say, a 16 bit integer. The maximum multiple of one data point before the stream ends, is < 2^32. The main restriction is that there isn’t enough memory to have an array of counters which completely covers the range of the data points (65536 counters of 0-2^32), much less record all single data points and bulk-process them afterwards. In the case where the dispersion of the data source covers the complete possible 16-bit range, the result is not of interest, i.e. this marks a histogram type which is not processed further. Valid histograms consist of only a few clusters where the majority of points are found. Data is roughly continuous which has a very valuable consequence: new outliers can, without loss of detection capability) supersede old outliers (i.e. those with the lowest count) so that new clusters can enter the histogram even when the available memory is full. This is very rare however, the data source is in a way nice to track; just the number and location of the clusters is unpredictable. The following is a try of mine with a binary tree recording the multitude of each data point (I didn’t implement the substitution, just the insert). The special property of the tree is that it tries to move points with a high occurrence number close to the root, in hope for a short search path in the majority cases. The boolean predicate is the function `exchange_p`

which compares the weight of a root to its left or right child. In case the predicate is true, an exchange is executed, possibly invoking further exchanges lateron.

The idea is that it is favorable to not exchange tree nodes at every insert but to let the node count run up to a certain multiple of its parent before an exchange is initiated, thereby avoiding unnecessary oscillations of nodes. Things worked out very differently, tho.

The problem exhibits a strange behaviour, with `QUOTA`

around 0.8 (i.e. exchange if root < 0.8*child) for the overall minimum number of operations. Is there some theory which amalgates O-notation with stochastics for special input distributions?

You can run the below example (it has real world data in it), the file is completely self-contained and should run out of the box.

`#include <cstdio> #include <cstdint> #include <cstdlib> int exchg; int ins; int tree_ins; float QUOTA = 1.0f; void error_func (const char *s) { printf ("%s", s); exit (1); } typedef enum { LEFT_CHILD, RIGHT_CHILD, NO_CHILD } child_side_t; typedef int16_t element_t; typedef uint32_t counting_t; struct bin_tree_counting_node_t { bin_tree_counting_node_t *left, *right; counting_t cnt; element_t element; }; void print_node (bin_tree_counting_node_t* root) { printf ("%i\t%u\n", root->element, root->cnt); } void print_tree (bin_tree_counting_node_t* root, int lvl) { if (root == NULL) return; print_tree (root->left, lvl+1); // printf ("Level %d: ", lvl); print_node (root); print_tree (root->right, lvl+1); } bool exchange_p (bin_tree_counting_node_t* root, bin_tree_counting_node_t* child, child_side_t side) { return (root->cnt < QUOTA * child->cnt); } bin_tree_counting_node_t* tree_insert_tree (bin_tree_counting_node_t* tree_a, bin_tree_counting_node_t* tree_b) { tree_ins++; if (tree_a == NULL) return tree_b; else if (tree_b == NULL) return tree_a; else if (exchange_p (tree_a, tree_b, NO_CHILD)) { if (tree_a->element < tree_b->element) tree_b->left = tree_insert_tree (tree_a, tree_b->left); else tree_b->right = tree_insert_tree (tree_a, tree_b->right); return tree_b; } // Case for a > b coincides with a ~ b // else if (exchange_p (tree_b, tree_a, NO_CHILD)) { // if (tree_a->element < tree_b->element) // tree_a->right = tree_insert_tree (tree_a->right, tree_b); // else // tree_a->left = tree_insert_tree (tree_a->left, tree_b); // return tree_a; // } else { if (tree_a->element < tree_b->element) tree_a->right = tree_insert_tree (tree_a->right, tree_b); else tree_a->left = tree_insert_tree (tree_a->left, tree_b); return tree_a; } } bin_tree_counting_node_t* exchange (bin_tree_counting_node_t* root, child_side_t side) { exchg++; // Exchange root with its child bin_tree_counting_node_t* child; if (side == LEFT_CHILD) { child = root->left; root->left = NULL; child->right = tree_insert_tree (root, child->right); } else { child = root->right; root->right = NULL; child->left = tree_insert_tree (root, child->left); } return child; } bin_tree_counting_node_t* tree_insert (bin_tree_counting_node_t* root, element_t elem) { ins++; if (root == NULL) { bin_tree_counting_node_t* new_node = (bin_tree_counting_node_t*)malloc (sizeof (bin_tree_counting_node_t)); if (new_node == NULL) { error_func ("Memory exhausted!"); } new_node->element = elem; new_node->cnt = 1; new_node->right = new_node->left = NULL; return new_node; } if (elem == root->element) { root->cnt++; if (root->cnt == 0) { error_func ("Counting overflow! Very large amount of inserts >2^32!"); } } else if (elem < root->element) { root->left = tree_insert (root->left, elem); if (exchange_p (root, root->left, LEFT_CHILD)) return exchange (root, LEFT_CHILD); } else { root->right = tree_insert (root->right, elem); if (exchange_p (root, root->right, RIGHT_CHILD)) return exchange (root, RIGHT_CHILD); } return root; } void free_tree(bin_tree_counting_node_t* root) { if (root == NULL) return; free_tree (root->left); free_tree (root->right); free (root); } int main (void) { element_t sample[] = { 17060,17076,17076,17060,17092,17028,17076,17060,17060,17076,17060,17076,17060,17060,17140,17140,17124,17124, 17124,17140,17108,17140,17124,17124,17108,17108,17124,17124,17140,17092,17124,17124,17140,17140,17124,17156, 17140,17108,17156,17140,17124,17124,17124,17108,17124,17124,17124,17092,17140,17092, 17124,17108,17156,17124,17156,17140,17124,17172,17124,17108,17124,17108,17108,17108,17108,17124,17108,17124, 17108,17108,17124,17124,17140,17124,17108,17092,17108,17108,17092,17124,17108,17108,17124,17108,17124,17108, 17124,17140,17156,17124,17108,17108,17124,17124,17124,17140,17092,17140,17124, 17108,17124,17124,17124,17124,17108,17124,17108,17124,17108,17108,17108,17124,17108,17124,17124,17108,17108, 17124,17108,17124,17140,17124,17124,17108,17108,17140,17140,17124,17108,17140,17124,16291,16339,16339,16307, 16323,16259,16275,16275,16259,16388,16388,16355,15795,15731,16195,16179,16179, 15715,14467,14643,14851,17284,17012,16147,15155,15203,16131,15331,14691,14739,14739,14755,14723,14739,14707, 14771,14739,14707,14691,14531,14787,14563,15587,15907,15907,15923,15907,13123,13107,13091,13267,13091,13187, 13091,14643,15875,15907,16964,16404,16227,15219,14771,14771,14803,14787,14803, 14787,14803,14803,14755,14755,14771,14755,14723,14723,14739,14739,14963,16884,16868,15827,13075,13123,13091, 12979,13043,13219,13075,13059,13075,13123,15779,15875,16916,17028,15155,14675,14707,14691,14707,14691,14691, 14691,14707,14691,14691,14691,14675,14707,14691,14675,14595,14595,14595,14563, 14547,14579,14611,14547,14515,14611,14595,14611,14595,14659,14659,14627,14643,14643,14659,14643,14643,14643, 14659,14659,14643,14643,14611,14659,14611,14659,14659,14659,14643,14643,14643,14643,14611,14643,14627,14675, 14627,14643,14531,14531,14499,15187,16884,16932,15891,15923,13107,13091,13043, 13059,13075,13027,13027,13059,13059,13587,13059,15763,16900,16932,14899,14595,14627,14659,14691,14691,14691, 14691,14659,14675,14675,14675,14675,14691,14675,14691,14675,14611,14643,15107,16788,16964,14835,13363,13059, 13075,13075,13043,13043,13043,13075,13059,13059,15475,15715,16884,16932,16964, 14707,14643,14675,14643,14611,14611,14611,14611,14627,14611,14611,14627,14627,14611,14595,14595,14595,14563, 15027,16756,16932,14595,13059,13075,13059,13059,13011,13027,13059,13059,13043,13059,15683,16852,16948,16067, 15267,14771,15875,16964,16996,16980,17012,17012,17028,17028,17076,17060,17044, 17060,17076,17076,17092,17076,17092,17092,17108,17124,17092,17108,17124,17108,17124,17124,17108,17140,17124, 17108,17124,17108,17028,17124,17124,17092,17124,17108,17124,17108,17124,17092,17108,17108,17108,17124,17124, 17140,17108,17124,17108,17124,17108,17108,17156,17124,17108,17092,17108,17092, 17108,17108,17124,17124,17108,17108,17108,17124,17108,17124,17108,17124,17124,17108,17124,17124,17124,17124, 17124,17092,17140,17108,17124,17124,17140,17028,17124,17028,17108,17108,17124,17124,17124,17124,17108,17108, 17124,17140,17044,17108,17028,17124,17124,17124,17108,17124,17124,17108,17124, 17092,17124,17124,17124,17108,17124,17124,17140,17124,17140,17140,17140,17124,17044,17124,17092,17140,17124, 17140,17124,17124,17124,17108,17124,17124,17124,17124,17124,17140,17076,17140,17140,17108,17140,17124,17140, 17140,17108,17108,17124,17108,17124,17124,17124,17108,17140,17124,17140,17060, 17124,17124,17188,17108,17124,17124,17140, }; for (QUOTA = 0.1; QUOTA < 3; QUOTA += 0.1) { ins = tree_ins = exchg = 0; bin_tree_counting_node_t *tree = NULL; for (int i=0; i<sizeof sample/sizeof sample[0]; i++) { tree = tree_insert (tree, sample[i]); } printf ("Q:\t%f\tins:\t%d\t tree_ins:\t%d\t exchg:\t%d\t sum:\t%d\n", QUOTA, ins, tree_ins, exchg, ins + tree_ins + exchg); //print_tree (tree, 0); //printf ("\n"); free_tree (tree); } return 0; } `

## Finding the Time Complexity – Worst Case (Big-Θ) – Array List, BST

Hi I’m a bit confused on how to find the time complexity of the following in the worst case in terms of big-Θ, I’ve figured out 1 and 2.

What is the worst-case time complexity, in terms of big-Θ, of each of these operations: (1) insert an element in the array list = **Θ(1)** (2) remove an element from the array list (e.g. remove an occurrence of the number 5) = **Θ(n)**

(3) remove the second element from the array list (i.e. the one in position 1)

(4)count the number of unique elements it contains (i.e. the number of elements excluding duplicates; e.g.[6,4,1,4,3] has 4 unique elements)

Suppose you have an initially empty array list with an underlying array of length 10. What is the length of the underlying array after:

(5) inserting 10 elements in the array list (6) inserting 10 more elements in the array list (i.e. 20 elements in total) (7) inserting 10000 more elements in the array list (i.e. 10020 elements in total)

What is the worst-case time complexity, in terms of big-Θ, of each of these operations on binary search trees: (8) add an element in the tree (assuming that the tree is balanced) (9) add an element in the tree (without assuming that the tree is balanced) (10) find the largest element in the tree (assuming that the tree is balanced) After each operation, we should still have a valid heap.

## What is Simple Uniform Hashing, and why searching a hashtable has complexity Θ(n) in the worst case

Can anyone explain nicely what Simple Uniform Hashing is, and why searching a hashtable has complexity Θ(n) in the worst case if we don’t have uniform hashing (where n is the number of elements in the hashtable)