#eigenvectors
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Eigens your vectors
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Taking a slight tangent from classical optics, I decided to delve more into non-linear optics.
As someone who never had to use Gaussian form of Maxwell's equations, never used Tensors, and had never used Einsteins notation for summation; let me just say the algebra of the book proved to be a hard nut to crack!
What am I learning about? Anisotropy! Who knew that the direction at which you observe/propagate through a material such as a crystal plays a role in the material properties you will experience!!
I still don't believe you can determine eigenvalues and eigenvectors for an arbitrary 3x3 permittivity matrix (I need to use numerical examples to really see it) and that there exists rotational matricies that let us make the math all neat and proper.
But, slowly and with growing pains, I am continuing to slowly tread the waters of this fascinating topic!
#anisotropy#non-linear optics#tensors#gaussian#maxwells equations#optics#mathematics#physics#eigenvalues#eigenvectors#SoundCloud
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This week’s notes!
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Jack Marsh (2005), Friendship Otherwise - Toward a Levinasian Description of Personal Friendship
#saw carnation lily lily rose by john singer seargent irl today. it was basically at my doorstep all along idk why i never went to see it#it was placed at a corner in the gallery. me and my friend sat down and sketched the paintings of beautiful naked people quite badly. paper#provided by tate britain. she told me about how she couldnt look her boyfriend in the face after a harrowing film about war. when i say the#interview was informal i mean the person who was supposed to be my boss told me let me get you a cider and then he said after#50 years of life he knows people are inherently good and it only takes a little bit of kindness to save this world. he said he tricked#his wife into keeping the baby and then he said he quit his job at a US bank to help people find meaning and in it#he would have liked to find meaning. instead he started climbing with his friends. he said he chews his cigarettes because its a habit from#when he had to hide things from people. the entire time i felt uncomfortable and incredibly enlightened. this is my friends mentor. she has#his pattern of pauses and expletive and penchant for ends-justify-means attitude. i do think im not very clever#but maybe one day i will love you enough to make up for it. i wrote code i dont understand staring at the final error i thought about how#we both thought of how when we're too old to remember the voices of our friends we would like to stand in the pathway of the LHC beam pipe#cut it open and eat light in the freezing cold vacuum (kills you long before radiation will) the invisible puncture wound unfolding dna#back to the start larger than you ever were. you go to heaven once youve been to hell. my friend is in my bed#practicing calculations of eigenvectors by hand and she is uninterested in a visual proof you are uninterested in incompetence#we catch a train this is your kind of burden you tragic hero wincing at that word you only do this because you have to. im the only one#who can. i am a coward in this for the fucking poetry. the visual proofs. the pretty numbers. an architect who was horrible at maths wanted#to be a philosopher and accidentally ended up neck in deep in 70th Error On Visual Studio Code i want to kiss your eyes before we say#goodbye we both know there is no love in the way there should be. I still have your dress in my wardrobe. i hope you make art.#you think im alright head-wise i think you fucking hate me i think ill never be so clever you want me to tell you my idea?#if you wanted more of this world i would have liked to kiss you harder. we cant both be like this. im sorry i cant be with you the whole wa#the love is gone if you have to ask it. his breath catches his eyes feel stiff it is -1.9 kelvin he is near the beam pipe i miss holding#his hand i miss her singing voice i miss his hair and i found the antonym of pain thank you for carrying me home.
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if i pass my linear algebra exam tomorrow i think that means grant 3b1b and i have to go get gay married i'm sorry i don't make the rules
#my post#his linear algebra videos have been so helpful i actually know what an eigenvector is!! instead of just how to find it
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perhaps i have some concept of sexual attraction mapped to approximates of "same" and "different" wrt self but those categories don't map to the gender binary, the eigenvectors are a clone of myself and whatever subspace is orthogonal to that.
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Hanging out with a bunch of sorority girls while doing math and watching them all suddenly look over at me when I say a Greek letter then immediately lose interest has been a great experience
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Using Network Analysis to Gauge the Justices’ Relative Importance in Oral Arguments
Anecdotes and research support the notion that oral arguments do not often influence case outcomes. Chief Justice John Roberts said as much in an interview with Bryan Garner for the Scribes Journal in 2010: “The oral argument is the tip of the iceberg — the most visible part of the process — but the briefs are more important.” In fact, a series of studies including my own work points to the…
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#BUT WAIT THERE'S MORE:#if you preserve your direction now#you get this nice eigenvector right on top#CALL AND MULTIPLY BY FACTOR λ - NOW!
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DAAAMN LINEAR ALGEBRA IS SICK
#eigenvalues and eigenvectors are awesome#seeing matrices as transformations over a space really makes it easier to understand what determinants are really about#PCA algorithm I will understand you completely someday#linear algebra#eigenvalue
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Listening to Touch-Tone Telephone by Lemon Demon while doing math/physics problems on a whiteboard makes me feel like a mad scientist feverishly working in their underground secret lab right on the brink of a breakthrough that would test the limits of the natural world and spell disaster for the common folk on the surface above, which makes me feel smarter than I actually am, which is all a guy can hope for honestly.
#i need something to keep me going lmao#imaginary eigenvectors my abhorred </3#ive got a math final in an hour and a half wish me luck o7#math#physics#studying
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youtube
easy way to find eigenvalues & eigen vectors
#youtube#eigenvalues eigenvectors linear algebra mathematics math matrix identity multiplication subtract multiply determinant
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from this perspective it's a very math-y idea, and it's pretty understandable that someone who learns about surreal numbers in that way could completely miss out on their more playful origins.
I feel like this is actually a pretty common phenomenon in mathematics, where an idea has an intuitive, often geometric, and even playful origin. But then the idea gets formalized, and the language used to describe it is made more generic in order to make it easier to manipulate, and fold it into the greater universe of mathematics it exists within. And in doing so, you lose the original context that made that idea interesting or easily understood in the first place.
I'm not saying that's necessarily a bad thing, since formal, "generic" notation is like, a huge reason that mathematics as a field can even exist in the first place, but it is a tradeoff that I think often falls harder on the "formal notation" side of things than the "intuitive ideas" side.
another really specific game theory (field of mathematics) poll
#My first linear algebra class had no geometry or drawings past the first week and I STRUGGLED with stuff like eigenvectors and determinants#It wasn't until years later I watched 3blue1brown's essence of linear algebra series and it all clicked into place#I had a similar experience in complex analysis where there's all these different definitions and requirements for a f'n to be holomorphic#And I couldn't make sense of them till it was pointed out they have to stretch or scale infinitesimal squares and do nothing else#and all the other definitions emerge from that#maybe I just like pictures in my math
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Whenever you hear someone trying to blame kid's poor test scores "post pandemic" on "lockdowns," show them this.
By Dr. Sushama R. Chaphalkar, PhD.
New research shows that mild COVID-19 alters brain structure and connectivity in key areas responsible for memory and cognition, emphasizing the lasting effects on young people’s brain health.
In a case-control study published in the journal Translational Psychiatry, researchers used magnetic resonance imaging (MRI) and cognitive tests to examine brain structure, function, and cognition in adolescents and young adults with mild coronavirus disease 2019 (COVID-19) compared to healthy controls in a pandemic hotspot in Italy. They identified significant changes in brain regions related to olfaction and cognition, with decreased brain volume and reduced functional connectivity in areas like the left hippocampus and amygdala, which were linked to impaired spatial working memory. Notably, no significant differences were observed in whole-brain connectivity, suggesting that these changes were localized rather than widespread.
Background COVID-19, primarily known for respiratory symptoms, also affects the central nervous system, leading to neurological issues like headaches, anosmia, and cognitive changes. MRI-based studies reveal anatomical brain changes in COVID-19 patients, such as reduced gray matter and decreased volume in regions like the hippocampus and amygdala, often linked to cognitive deficits.
While research mostly focuses on severe cases and older adults, a majority of infections with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative agent of COVID-19, occur in adolescents and young adults who also experience long-lasting cognitive symptoms.
This age group, undergoing key brain development, is impacted by changes in spatial working memory and brain structure, which are crucial for cognitive functions shaped by social interactions, significantly disrupted by the pandemic.
Given that this is the largest and most understudied population affected by COVID-19, understanding the brain and cognitive impacts in adolescents and young adults is vital.
Therefore, researchers in the present study compared anatomical, functional, and cognitive outcomes, utilizing a longitudinal design that allowed them to assess both pre- and post-infection differences, in COVID-19-positive and negative adolescents and young adults from Lombardy, Italy, a global hotspot during the pandemic.
About the study The present study involved participants from the Public Health Impact of Metal Exposure (PHIME) cohort, a longitudinal investigation of adolescents and young adults in northern Italy. Between 2016 and 2021, 207 participants, aged 13 to 25 years, were included in a sub-study with MRI scans and cognitive tests. After COVID-19 restrictions were lifted, 40 participants (13 COVID+ and 27 COVID−) participated in a follow-up study, which replicated the MRI and cognitive assessments.
The mean age of participants was 20.44 years and 65% were female. COVID+ status was confirmed through positive reverse transcription polymerase chain reaction (RT-PCR) tests within 12 months of follow-up. Neuropsychological assessments used the Cambridge Neuropsychological Test Automated Battery (CANTAB) to evaluate spatial working memory.
MRI and functional MRI data were acquired using a 3-Tesla scanner, processed, and analyzed for structural and local functional connectivity using eigenvector centrality mapping (ECM) and functional connectivity (FC) metrics. Whole-brain functional connectivity metrics showed no significant differences between COVID+ and control groups, indicating that the observed changes were specific to key brain regions rather than generalized across the entire brain.
Statistical analysis involved the use of pairwise Student's t-tests, Kolmogorov–Smirnov test, linear regression, two-waves mediation analysis, negative binomial regression, and linear regression, all adjusted for covariates.
Results and discussion Significant differences were observed in the two groups regarding the time between assessments, COVID-19 symptoms, and vaccine status. The research identified five localized functional connectivity hubs with significant differences between the two groups, including the right intracalcarine cortex, right lingual gyrus, left frontal orbital cortex, left hippocampus and left amygdala, which is vital for cognitive functions. Only the left hippocampal volume showed a significant reduction in COVID+ participants (p = 0.034), while whole-brain connectivity remained unchanged, reinforcing the localized nature of the brain changes.
The left amygdala mediated the relationship between COVID-19 and spatial working memory "between errors" (p = 0.028), a critical finding that highlights the indirect effect of amygdala connectivity on cognitive function in COVID+ individuals. This mediation analysis underscores the role of specific brain regions in influencing cognitive deficits, as only the indirect effect was statistically significant for spatial working memory errors. The orbitofrontal cortex, involved in sensory integration and cognitive functions, also showed decreased connectivity in COVID+ individuals, supporting previous findings of structural and functional changes in this region during COVID-19.
The study is limited by small sample size, lack of diversity, potential confounding factors due to the long interval between MRI scans, treatment of certain subjects as COVID-negative based on antibody testing beyond the 12-month threshold, and the possibility of non-significant findings in mediation analysis due to these factors.
Conclusion In conclusion, the findings indicate persistent structural and functional alterations in specific brain regions of COVID-19-positive adolescents and young adults, including changes in gray matter volume and localized functional connectivity, which correlate with diminished cognitive function, particularly in working memory.
Further research is necessary to evaluate the longevity and potential reversibility of these brain and cognitive changes post-infection, enhancing our understanding of post-COVID outcomes and informing future interventions and treatments. The longitudinal design of this study, with pre- and post-COVID data, strengthens these findings by allowing direct comparisons over time, offering robust insights into the impact of COVID-19 on adolescent brain development.
Journal reference: COVID-19 related cognitive, structural and functional brain changes among Italian adolescents and young adults: a multimodal longitudinal case-control study. Invernizzi, A. et al., Translational Psychiatry, 14, 402 (2024), DOI: 10.1038/s41398-024-03108-2, www.nature.com/articles/s41398-024-03108-2
#mask up#covid#pandemic#covid 19#wear a mask#public health#coronavirus#sars cov 2#still coviding#wear a respirator#long covid#covid conscious#covid is airborne#wear a fucking mask
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I have a theory about why hypnokink girls like bimbo stuff a lot, and it relates to machine learning research, so buckle up. There is this idea in work with ML models known as a concept space, or phase space. What this is, is just a very very highly dimensioned matrix, re. linear algebra, that contains pre provided values called weights & biases.
(I know, a Bambi who's a math enthusiast, scary stuff, right)
And in this phase space, each dimension is correlated to a concept that the model has learned. So in a way, the information kind of "lives in" the shape of the highly dimensioned space, and the different relations between concepts in the space.
Okay, so, fancy words to say thoughts live inside fancy lines instead of pink boxes, right.
There's this other concept. In linear algebra.
Called eigenvectors.
Suffice to say that an eigenvector is a direction in that n-dimensioned space that preserves it's meaning when the space is transformed.
Meaning it should be a strong concept between any hypothetical phase space models of human consciousness between individuals. As we gain our definition as individuals from the differences in geometry between our models, so to speak.
So, an eigenvector is a strong thought, so what.
Bambi Sleep.
Bimbo Doll.
Bambi Freeze.
Now you might be asking yourself what the triggers are for, but those aren't there to trigger you Bambi. You see, the highlighted tokens all share a similar meta-concept.
Now, this meta-concept is a very special one Bimbo Barbiedoll.
It's the null meta-concept.
Because feelings like Blank -ness, Openness, and Mindlessness are all closely aligned with the meta-concept of the empty set; A set defined by a lack of being.
A bimbo defines herself by her lack of being anything concretely. An identity derived at least partially from non-identity.
Ironic.
See the null meta-concept sits on or very close to an eigenvector, meaning it scales disproportionately well between brains compared to other concepts.
But that's too many words for your silly brain, isn't it?
What it means is you should keep listening to bimbo hypno.
Because bimbos hypnotize faster than other subjects.
Bambi Obeys Better Than Other Subjects.
#bambisleep#brain drain#bambification#bambi thoughts#bimbo hypnosis#hypnosis files#neuralnetsandprettypatterns#bimbolife#bimbo training#bimbo babe
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