# rss_item

guid: https://math.stackexchange.com/q/5044424
title: Does a line have more points than a line segment?
author: optmstpessmst
url: https://math.stackexchange.com/questions/5044424/does-a-line-have-more-points-than-a-line-segment
feedurl: https://math.stackexchange.com/feeds
content:
            <p>Just a thought experiment; both a line and a line segment both contain infinite points. However, shouldn't a line segment contain fewer points compared to a line, since a line segment has two definite endpoints, while a line does not? My thought was that if i had a line segment of length x, a line could contain infinite copies of that line segment with length x. When looking online, there were two arguments:</p>
<ul>
<li>A line segment has less points than a line because a line has an infinite length while a line segment has a finite length (my thought process.)</li>
<li>A line segment has the same amount of points as a line because both have infinite points.</li>
</ul>
<p>Both seem to make sense to me. (For reference, I do not know any math past calculus.)</p>

        


guid: https://math.stackexchange.com/q/5044426
title: Finding radius of circle from two arbitrary intersecting chords
author: Rabid
feedurl: https://math.stackexchange.com/feeds
url:
https://math.stackexchange.com/questions/5044426/finding-radius-of-circle-from-two-arbitrary-intersecting-chords

content:
            <p>From the intersecting chords theorem, we know ab = cd where a and b make up one chord and c and d make up the other chord.  I am wondering if just given a,b,c,d, can we find the radius of the circle that contains the chords in terms of a,b,c,d only?</p>
<p>From this MathSE post <a href="https://math.stackexchange.com/questions/1789732/find-radius-of-a-circle-from-intersecting-chords">Find radius of a circle from intersecting chords</a>, I understand that if we were given the distance x between the point of intersection of the chords and the center the circle, then we can find the radius.  But is there a way to express this distance x in terms of a,b,c,d? Is there a way to find radius without needing this distance x?</p>
<p>I think I can solve if the chords were perpendicular but that is a special case, and I wonder if this can be solved for non-perpendicular intersecting chords.  I feel like it should be possible also because it is possible to solve for a circle's center and radius given 3 points on a circle, but I am not sure for this problem.</p>

        


guid: https://math.stackexchange.com/q/5044427
author: shuriken
feedurl: https://math.stackexchange.com/feeds
title:
If A is positive definite, B is self adjoint, and AB+BA is positive definite, then B is positive definite.

url:
https://math.stackexchange.com/questions/5044427/if-a-is-positive-definite-b-is-self-adjoint-and-abba-is-positive-definite-th

content:
            <p>Suppose A and B are complex linear operators of some finite dimensional vector space <span class="math-container">$X$</span>. In my definition, positive definite operators are only for self adjoint operators.</p>
<p>If A is positive definite, B is self adjoint, and AB+BA is positive definite, I want to show that B is also positive definite.</p>
<p>I have tried various kinds of inner product combination such as <span class="math-container">$\langle B(AB+BA)x,x \rangle$</span> to try to reach a conclusion that <span class="math-container">$\langle Bx,x \rangle &gt; 0$</span> for all <span class="math-container">$x$</span> but I have’t been successful. Any hints or help would be greatful!</p>

        


guid: https://math.stackexchange.com/q/5044428
title: Taylor Expansion of a Functional Involving Matrix Evolution
author: Mike
feedurl: https://math.stackexchange.com/feeds
url:
https://math.stackexchange.com/questions/5044428/taylor-expansion-of-a-functional-involving-matrix-evolution

content:
            <p>For a function <span class="math-container">$f(x)$</span>, the <em>Taylor series expansion</em> around <span class="math-container">$x$</span> is given by<br />
<span class="math-container">\begin{equation}  
f(x + dx) \approx f(x) + f'(x) dx + \frac{f''(x)}{2} (dx)^2 + \frac{f'''(x)}{6} (dx)^3 + \dots  
\end{equation}</span></p>
<p>Now, consider a function of time <span class="math-container">$t &gt; 0$</span> defined as<br />
<span class="math-container">\begin{equation}  
F(\textbf{R}(\theta, t)) = \operatorname{tr} \left( \textbf{X}^2~ \textbf{R}(\theta, t) \right),  
\end{equation}</span><br />
where the matrix <span class="math-container">$\textbf{X}$</span> is implicitly determined by the equation<br />
<span class="math-container">\begin{equation}  
\frac{\partial \textbf{R}(\theta, t)}{\partial \theta} = \frac{1}{2} \left( \textbf{X} \textbf{R}(\theta, t) + \textbf{R}(\theta, t) \textbf{X} \right).  
\end{equation}</span></p>
<p><strong>Question:</strong> Suppose the function <span class="math-container">$\textbf{R}(\theta, t)$</span> evolves over time such that for a small increment <span class="math-container">$dt$</span>, it changes from <span class="math-container">$\textbf{R}(\theta, t)$</span> to <span class="math-container">$\textbf{R}(\theta, t+dt)$</span>. How can the Taylor series expansion in equation (1) be adapted to describe the behavior of <span class="math-container">$F(\textbf{R}(\theta, t+dt))$</span> in this case?</p>

        


guid: https://math.stackexchange.com/q/5044430
title: What is the computational complexity of empirical statistical distances?
author: Resu
feedurl: https://math.stackexchange.com/feeds
url:
https://math.stackexchange.com/questions/5044430/what-is-the-computational-complexity-of-empirical-statistical-distances

content:
            <p><strong>Setup.</strong> Given 2 samples of size <span class="math-container">$n$</span> and each datapoint has feature dimension <span class="math-container">$d$</span> -- the goal is to compute the statistical distance between the 2 samples. This can be done using the earth mover's distance (EMD) and the maximum mean discrepancy (MMD).</p>
<p><strong>Question.</strong> What is the runtime complexity of computing statistical distances like the EMD and the MMD when we take into account the feature dimension?</p>
<p><strong>My attempt.</strong> If <span class="math-container">$d$</span> is a constant, then:</p>
<ul>
<li>by <a href="https://home.ttic.edu/%7Essameer/Research/Papers/WEMD_CVPR08.pdf" rel="nofollow noreferrer">Orlin's algorithm</a>, the runtime complexity for EMD is <span class="math-container">$O(n^3\log n)$</span>.</li>
<li>By the <a href="https://www.stat.cmu.edu/%7Elarry/=stat705/Lecture27.pdf" rel="nofollow noreferrer">estimation formula</a> of MMD, the runtime complexity for MMD is <span class="math-container">$O(n^2)$</span>. Looking at the formula, I suspect it should be <span class="math-container">$O(dn^2)$</span> -- is this correct?</li>
</ul>
<p>So what happens if <span class="math-container">$d$</span> is not a constant? Or does <span class="math-container">$d$</span> not matter in the computation of runtime complexity? I've noticed that previous works usually ignore the feature dimension in the computational complexity -- why is this the case?</p>

        


guid: https://math.stackexchange.com/q/5044432
title: application of MLE for average rate of change data
author: 박동진.
url: https://math.stackexchange.com/questions/5044432/application-of-mle-for-average-rate-of-change-data
feedurl: https://math.stackexchange.com/feeds
content:
            <p>I<code>m trying to esimates some state variable, f(t) from  dA(t)/dt = (Bexp(-(lamda1)t)+ (1-B)exp(-(lambda2)t))/ 2+ 2cosh(m(f(t)+F))*  with known value B, lambda, m, F since it is not integrable(or at least i can</code>t), i`m trying to use A(t+delta)-A(t)/delta, the  average rate of change as observed data.
Am i good to go like this? is there any former article used this kind of method?</p>

        


guid: https://math.stackexchange.com/q/5044433
title: Complements and logical consequence
author: Daniel Aricatt
url: https://math.stackexchange.com/questions/5044433/complements-and-logical-consequence
feedurl: https://math.stackexchange.com/feeds
content:
            <p>If <span class="math-container">$\Gamma\models\alpha$</span> then does <span class="math-container">$\Gamma^c\models\neg \alpha$</span>. Where <span class="math-container">$\Gamma^c$</span> is the complement of <span class="math-container">$\Gamma$</span> in the language.</p>
<p>I split it up into cases and the only case to be resolved is when <span class="math-container">$\alpha$</span> and <span class="math-container">$\neg\alpha$</span> both belong to <span class="math-container">$\Gamma$</span>. In this case <span class="math-container">$\Gamma\models\alpha$</span> is vacuously true but how would I proceed to show that right side of the implication is false/true?</p>

        


guid: https://math.stackexchange.com/q/5044443
title: Computing the discriminant of the number field $\mathbb Q(\alpha)$, where $\alpha^5=2.$
author: shwsq
feedurl: https://math.stackexchange.com/feeds
url:
https://math.stackexchange.com/questions/5044443/computing-the-discriminant-of-the-number-field-mathbb-q-alpha-where-alph

content:
            <p>I want to compute the discriminant of the number field <span class="math-container">$K:=\mathbb Q(\alpha)$</span>, where <span class="math-container">$\alpha^5=2.$</span></p>
<p>I guess that <span class="math-container">$\{1,\alpha,\alpha^2,\alpha^3,\alpha^4\}$</span> is an integral basis of <span class="math-container">$\mathcal O_K,$</span> however I compute that <span class="math-container">$4\mid \mathrm{Disc}(1,\alpha,\alpha^2,\alpha^3,\alpha^4)$</span>, so it has square factors, and I can't claim that <span class="math-container">$\{1,\alpha,\alpha^2,\alpha^3,\alpha^4\}$</span> is an integral basis.</p>
<p>Can someone give some hints? Many thanks in advance!</p>

        


guid: https://security.stackexchange.com/q/280743
title: Facebook signups using our company domain
author: Marji Akshenay
url: https://security.stackexchange.com/questions/280743/facebook-signups-using-our-company-domain
feedurl: https://security.stackexchange.com/feeds
content:
            <p>For the past few days, we've been receiving emails to our catch-all domain about signups to Facebook.</p>
<p>The emails are simple confirmation emails with a code to confirm the email ownership and do indeed originate from Facebook:</p>
<pre><code>We got your request to create an account. Here’s your confirmation code:
FB-XXX
Don't share this code with anyone.
If someone asks for this code
Don't share this code with anyone, especially if they tell you they work for Facebook or Meta.
</code></pre>
<p>The attacker is using random strings and registers a few Facebook accounts a day in different countries.</p>
<p>I am wondering what is happening here. I am able to view the account on Facebook as the email provides a link to them. They have no profile picture and no visible activity.</p>
<p>Any idea of what they're trying to accomplish?</p>

        


guid: https://security.stackexchange.com/q/280762
title: What does the parallelism parameter in memory-hard password hashing algorithms adjust?
author: The Death Sidius
feedurl: https://security.stackexchange.com/feeds
url:
https://security.stackexchange.com/questions/280762/what-does-the-parallelism-parameter-in-memory-hard-password-hashing-algorithms-a

content:
            <p>When I change the parallelism parameter on Scrypt or on Argon2, which processing unit's threads do I influence? The CPU's threads? The GPU's threads? How does this all work?</p>

        


guid: https://security.stackexchange.com/q/280767
title: HTTP 2 not possible without certificate?
author: Alex
url: https://security.stackexchange.com/questions/280767/http-2-not-possible-without-certificate
feedurl: https://security.stackexchange.com/feeds
content:
            <p>It appears that http 2 requires TLS. Which is fine, but why are certificates mandatory?
From what I know you can have TLS without certificates. Certificates just add an extra layer of security. How can we test HTTP 2 on localhost if certificate is mandatory? Localhost cannot obtain certificate...</p>

        


guid: https://security.stackexchange.com/q/280771
title: Hashing user input data redunant on https?
author: Alex
url: https://security.stackexchange.com/questions/280771/hashing-user-input-data-redunant-on-https
feedurl: https://security.stackexchange.com/feeds
content:
            <p>Consider a web app that allows the user to upload files to a server. While uploading files, the app will generate hashes from the file content and send that hash to the server, along with the actual file content. Server will also generate a hash from the received file content, and compare it with the hash it received from the web app. This is done for checking file integrity, making sure the uploaded file is the same as the original.</p>
<p>But with https, is this unnecessary? Https encrypts any data with a key, so if something was altered during transfer, the decryption on the server would fail, right?</p>

        


guid: https://security.stackexchange.com/q/280774
author: Heinzi
feedurl: https://security.stackexchange.com/feeds
title:
What's the deal with CISA adding CVE-2024-49035 (Microsoft Partner Center vulnerability) to its catalog of exploited vulnerabilities?

url:
https://security.stackexchange.com/questions/280774/whats-the-deal-with-cisa-adding-cve-2024-49035-microsoft-partner-center-vulner

content:
            <p>Two weeks ago (Feb 25, 2025), CISA <a href="https://www.cisa.gov/news-events/alerts/2025/02/25/cisa-adds-two-known-exploited-vulnerabilities-catalog" rel="nofollow noreferrer">added</a> CVE-2024-49035 to its catalog of actively exploited vulnerabilities.</p>
<p>Now, the thing is: CVE-2024-49035 is not a &quot;classic&quot; vulnerability in a software product where admins need to take action and install a patch. It's an old (Nov 2024) vulnerability in a Microsoft web service (their &quot;partner portal&quot;) which, according to Microsoft, <a href="https://msrc.microsoft.com/update-guide/vulnerability/CVE-2024-49035" rel="nofollow noreferrer">requires no customer action to resolve</a>.</p>
<p>If this issue has been fixed in Nov 2024 (by Microsoft fixing their cloud service), how can it be &quot;actively exploited&quot; in Feb 2025? As a system administrator who (occasionally) uses partner.microsoft.com to download software, I'm unsure how CISA expects me to react.</p>

        


guid: https://security.stackexchange.com/q/280776
author: Geek
feedurl: https://security.stackexchange.com/feeds
title:
What are some reliable and well-maintained Post-Quantum Cryptography (PQC) libraries with Go support? [closed]

url:
https://security.stackexchange.com/questions/280776/what-are-some-reliable-and-well-maintained-post-quantum-cryptography-pqc-libra

content:
            <p>I am looking for reputable libraries or solution providers that offer reliable, well-maintained, and well-documented implementations of post-quantum cryptographic (PQC) algorithms. Specifically, I am interested in:</p>
<ul>
<li>Digital signature schemes (e.g., MLDSA, SL-DSA, Falcon)</li>
<li>Hashing functions</li>
<li>Symmetric encryption</li>
<li>Key establishment and key encapsulation mechanisms (e.g., Kyber)</li>
</ul>
<p>Ideally, the library should have:</p>
<ul>
<li>Support for multiple programming languages, with a preference for <strong>Go (Golang)</strong></li>
<li>A strong reputation in the cryptography community</li>
<li>Regular updates and active maintenance</li>
<li>Comprehensive documentation and security audits</li>
</ul>
<p>Given that PQC is an evolving field with changing standards and ongoing refinements, what should be the key <strong>evaluation criteria</strong> when selecting a library for production use? Some factors I have considered include:</p>
<ul>
<li><strong>Security and Trustworthiness:</strong> Has the library undergone independent audits or been endorsed by recognized security bodies?</li>
<li><strong>Community Adoption:</strong> Is the library widely used or actively maintained?</li>
<li><strong>Performance:</strong> Is it efficient enough for real-world use cases?</li>
<li><strong>Interoperability:</strong> Does it integrate well with existing cryptographic libraries and protocols?</li>
<li><strong>Flexibility &amp; Future-proofing:</strong> How adaptable is the implementation to changes in PQC standards?</li>
</ul>
<p>Any recommendations would be greatly appreciated!</p>
<p>If anyone has any experience using such a library, that would be tremendously valuable..</p>

        


guid: https://security.stackexchange.com/q/280780
title: Can one buy Van Eck Phreaking equipment?
author: user352629
url: https://security.stackexchange.com/questions/280780/can-one-buy-van-eck-phreaking-equipment
feedurl: https://security.stackexchange.com/feeds
content:
            <p>I heard about the method and think that my neighbour is using this technology on me. Is it possible for private persons to get the equipment at all?</p>

        


guid: https://security.stackexchange.com/q/280783
author: Agritite
feedurl: https://security.stackexchange.com/feeds
title:
Windows Application Directory Attack for elevated programs implicitly linking dlls: is it the user's responsibility or the developer's?

url:
https://security.stackexchange.com/questions/280783/windows-application-directory-attack-for-elevated-programs-implicitly-linking-dl

content:
            <p>I'm talking about the 'Application Directory Attack' on Windows, where the attacker plants a dll which an executable depends, into the same folder as the executable, and when the user executes it, the rogue dll is loaded.</p>
<p>Many previous posts has already established that, &quot;If the attacker already has write permission to the application directory, then he might as well just replace the contents of the entire executable with his payload. Why bother planting a dll?&quot;</p>
<p>Example 1: <a href="https://stackoverflow.com/questions/28634528/dll-preloading-attack-kernel32-dll-loads-system-libraries-from-application-dire">DLL preloading attack. kernel32.dll loads system libraries from application directory</a></p>
<p>Example 2: <a href="https://stackoverflow.com/questions/46180293/how-to-stop-dll-hijacking-for-secondary-implicitly-loaded-dlls">How to stop DLL Hijacking for secondary IMPLICITLY loaded DLLs</a></p>
<p>Even Raymond Chen has several posts about it:</p>
<p><a href="https://devblogs.microsoft.com/oldnewthing/20121207-00/?p=5893" rel="nofollow noreferrer">https://devblogs.microsoft.com/oldnewthing/20121207-00/?p=5893</a></p>
<p>and</p>
<p><a href="https://devblogs.microsoft.com/oldnewthing/20161013-00/?p=94505" rel="nofollow noreferrer">https://devblogs.microsoft.com/oldnewthing/20161013-00/?p=94505</a></p>
<p>Surely, programs should be installed in Program Files to avoid that. How about elevated installers? Clearly you need an elevated installer to write to Program Files; how about portable elevated utilities? My question would be:</p>
<p>Is it the user's responsibility to make sure to save and execute any elevated program in a secure directory, or is it the developer's responsibility to make sure it only loads genuine dlls? This is explicitly asking about Windows, not a general principal that applies on all OSes.</p>
<p>For example there's recently a <a href="https://intruceptlabs.com/2025/02/zero-day-vulnerability-in-microsoft-sysinternals-tools/" rel="nofollow noreferrer">claimed vulnerability report</a> (source <a href="https://www.reddit.com/r/blueteamsec/comments/1igqb8n/dll_hijacking_zeroday_vulnerability_in_microsoft/?rdt=42828" rel="nofollow noreferrer">here</a>) against Microsoft's Sysinternals Suite, which from the news article it seems like Microsoft closed it as &quot;not a vulnerability but a defense-in-depth issue&quot;. I tested Process Monitor and it indeed does implicitly link to several Windows Dlls not on the KnownDll list:</p>
<pre><code>&gt;&gt; dumpbin /dependents procmon64.exe
Dump of file procmon64.exe

File Type: EXECUTABLE IMAGE

  Image has the following dependencies:

    WS2_32.dll
    VERSION.dll
    COMCTL32.dll
    FLTLIB.DLL
    KERNEL32.dll
    USER32.dll
    GDI32.dll
    COMDLG32.dll
    ADVAPI32.dll
    SHELL32.dll
    ole32.dll
    OLEAUT32.dll
    SHLWAPI.dll
    UxTheme.dll
    dwmapi.dll
    ntdll.dll
</code></pre>
<p>So is this to say that Process Monitor has an application directory attack vulnerability? Another example is Visual Studio Code. It is a per-user installation, so it resides in <code>%LOCALAPPDATA%</code>. Like all electron apps, <code>code.exe</code> bundles <code>ffmpeg.dll</code> in the same directory. Is this to say Vscode also has an application directory attack vulnerability? Running Vscode with elevation is not unheard of, due to for example running tests that require elevation.</p>
<p>The reason I'm asking this is that an elevated utility I participated in development recently received a similar vulnerability report, and I'm inclined to not fix it because, well Vscode never &quot;fixed&quot; it, nor did Sysinternals. Also as previously stated, &quot;fixing&quot; this doesn't make the system any safer; if the attacker already gains normal user privilege, then there are loads of other attack vectors to use; why bother with this one? Ultimately any attempt would still require user interaction, therefore no boundaries breached.</p>
<p>On the other hand, some of my other collaborators claim that &quot;If the executable is code-signed with a certificate, then the developers should be responsible for making sure it can't be taken advantage in any attack attempts.&quot;</p>
<p>Is there a general view on this matter? Or perhaps an official statement from Microsoft?</p>

        


guid: https://security.stackexchange.com/q/280784
title: URL Redirection from Malicious Domain
author: Learner
url: https://security.stackexchange.com/questions/280784/url-redirection-from-malicious-domain
feedurl: https://security.stackexchange.com/feeds
content:
            <p>A legitimate web application has been deployed using Apache 2.4.3 and PHP 7.4.2, and it is hosted on a public DNS. The application operates smoothly; however, I received an advisory from a security firm indicating that my web application is being exploited by a malicious domain. Upon investigating the domain, like abc.xyz, I found that it redirects requests to my web application, resulting in a 302 HTTP response. Despite having a Web Application Firewall and a standard firewall in place, not able to block/prevent the request.
Seeking kind expert opinion.</p>

        


