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Are you an Undergraduate, Masters Degree, or PhD student or completing a Post Doc and need assistance analysing your research data or interview transcripts?, I can code transcript contents into nodes, relevant child nodes (themes) and analyse the relationship or correlations that exist between themes. I will analyze your qualitative data.

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of mice and men analysis essay

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of mice and men analysis essay

Analysis of Basic Recursive Functions

I’m trying to understand the contrast between run-time for this function

public static String f(int N) {     if (N == 0) return "";     String s = f(N / 2);     if (N % 2 == 0) return s + s;     else            return s + s + "x"; } 

and this function

public static String f(int N) {     if (N == 0) return "";     if (N == 1) return "x";     return f(N/2) + f(N - N/2); } 

where string concatenation takes time proportional to the size of the strings.

So far, I believe that the first function is called log(N) times for input N and the second 2log(N) times. Is that right? Beyond that, I’m not sure how to think about how many operations happen in each of those calls. I know that for the first function, in the base case there are 0 operations (no concatenation), then 1 operation (concatenation of two null strings with a string of length 1?), then 2 operations. In general I believe the string produced by a call with N is of length N? But I just don’t know where to start thinking about how it all adds up.

For the second one likewise I’m a little lost. I just need a way to approach the analysis. Keep in mind I’m not great with symbols, so if you’re going to show off with symbols, I’d appreciate an explanation that will help me follow the symbols as well.

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Analysis quickselect: Median of Medians with duplicates

in This Lecture Notes 1 (page 3), it is said concerning quickselect with median of medians:

If there are repeated elements … Alternatively, one has to refine the algorithm and the analysis (see CLR).

But in my copy of CLRS (2011), the authors assumed that the elements are distinct.

How would one refine the algorithm and the analysis?

(I’m aware that you can make elements distinct in O(n), but I’m interested in the alternative)

[1] – https://people.eecs.berkeley.edu/~luca/w4231/fall99/slides/l3.pdf

Connection between Schur multipliers in representation theory and functional analysis?

I was wondering if there is any connection between two things called Schur multipliers or is it just a coincidence? Namely, in representation/group theory the Schur multiplier of a group $ G$ is its second homology group $ H_2(G, \mathbb{Z})$ . In functional analysis a function $ \varphi \colon \mathbb{N} \times \mathbb{N} \to \mathbb{C}$ is a Schur multiplier if for any bounded linear operator $ A: l^2 \to l^2$ with matrix $ (a_{i,j})_{i,j \in \mathbb{N}}$ (with respect to the standard orthonormal basis of $ l^2$ ) the matrix $ (\varphi(i,j)a_{i,j})_{i,j \in \mathbb{N}}$ defines a bounded linear operator.

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Analysis of hacked servers — daily RDP connections I can’t find an obvious reason for

I’m cleaning up after an incident where a few servers were hacked. A new IDS has been put in place, the firewall has been upgraded, the services used in the attack are being replaced with more secure alternatives, and everything that doesn’t need to be exposed is now behind a VPN, so at this point my focus is on determining what was going on while these servers were hacked. This is interesting to me and I wonder if any of you have seen something like it.

The hack started with RDP brute force and created a second account and then spread over RDP as far as it could using the same credentials and whatever it could dump from the first server. Then, for a period of several months, the hackers connected a few times a day over RDP for anywhere from a few seconds to a few minutes on both of those accounts. To try to figure out what might have been going on, I’ve:

  • Run sleuthkit against the drives
  • Written a tool to sequence the file timeline against all useful event logs and group those by remote session intervals and also run other profiling on the sessions
  • Reviewed the users on the box
  • Scanned the box
  • Looked at all services listening on any port
  • Manually gone through the files

I haven’t set something up to listen for odd traffic to or from these boxes since we’ve taken them offline and I’m working with them as disconnected VMs.

Apart from some signs one of the boxes might have been temporarily used to stage a social engineering attack, I haven’t seen any activity of note during the entire time the boxes are actively hacked. I don’t imagine a higher form of access is taking place since the RDP connections were so active, and based on the firewall and services that were still working, the only form of backdoor I can think of actually working without detection would be a reverse shell, and if that existed, I’m not sure why RDP would be so active.

It turns out that one of the servers hacked by the hacked server had also been hacked the same way several months prior (by IPs from the same region), and that exhibited the same sort of usage: daily short RDP connections from the same set of sources after the source rotation from the brute force attacks had finished, but nothing odd on the box itself.

I suppose the continued connections could be just validation of current account credentials and access levels, but I’d have to imagine more would have been going on that I’m not seeing in the logs or file audits. Does anyone have any related experiences they’d like to share lessons learned from?


Stability Analysis of a differential equation

My question is about stability analysis and whether the equilibrium point is well-defined in example 2?. If they are not defined, how can one approach the stability analysis for those cases.

Example 1:

$ \frac{dx}{dt} = -x + c$

In this example, $ c$ is a constant and $ x=c$ is an asymptotically stable equilibrium point. If $ x<c$ , $ \frac{dx}{dt}$ will be positive, pushing $ x$ toward $ c$ and a similar statement holds for the negative case. In this case, the equilibrium point is well defined.

Example 2: We have a slightly modified equation:

$ \frac{dx}{dt} = -x + c(1-\frac{1}{M}\exp(-2t))$

and M is a very large positive constant. No matter where we start from, we’ll always approach $ c$ . Can we say $ x=c$ is also an equilibrium point in this case? The problem is when we plug this value in the equation $ \frac{dx}{dt}$ will not be zero at any time. My understanding is for an equilibrium point, we must be able to plug in the state at the equilibrium point and observe that it doesn’t change.

Static analysis technique

Is there a static analysis technique work as follows: given a variable, e.g. string s = "...", the technique can find (approximately) all the possible values of string s via static analysis?

If this technique exists, what is the name of this technique? Thanks in advance!

BTW, I am trying to find a tool using this technique which supports PHP, please let me know if you know there is such a tool…