Difference between r1.129 and the current
@@ -441,7 +441,7 @@
=== ring counter ===
curr at [[원핫%2Cone-hot?action=highlight&value=counter]]
[#countable]
countability n.
curr at [[원핫%2Cone-hot?action=highlight&value=counter]]
[#countable]
== countability #countable =
== countability #countable ==
countable adj.countability n.
@@ -493,12 +493,20 @@
allocator
Srch:allocator
== memory allocator ==
[[memory_allocator]] =,memory_allocator =,memory_allocator . memory_allocator
[[메모리할당자,memory_allocator]] ? [[메모리,memory]]를 [[할당,allocation]]하는 i.e. [[메모리할당,memory_allocation]]하는
=== slab allocator ===
[[slab_allocator]] =,slab_allocator . slab_allocator
[[WtEn:slab_allocator]]
Srch:allocator
== memory allocator ==
Ggl:"memory allocator"
Bing:"memory allocator"
"memory allocator"
'''memory allocator'''
메모리할당자
메모리할당기
중에?
w l
https://en.wiktionary.org/wiki/memory_allocator x 2024-06
// memory allocator .... Ggl:"memory allocator" Bing:"memory allocator" NN:"memory allocator"
Srch:memory_allocatorUp: allocator( [할당자,allocator] or [할당기,allocator] or 얼로케이터 )
[[slab_allocator]] =,slab_allocator . slab_allocator
[[WtEn:slab_allocator]]
@@ -645,33 +653,65 @@
[#sort]
= sort / sorting / 정렬 #sort =
(대충 생각나는대로,chk) { [[키,key]]를 기준으로(primary_key 말고 secondary_key ...도 있는 경우가 있는데 tbw) , [[비교,comparison]]하여, (근데 Ggl:"비교정렬" 이 아닌 경우도 있는데 tbw) [[순서,order]]에 따라, 위치를 바꾸어서(교환, swap, exchange) }
Sub:
radix
[[radix_sort]] ... curr at [[래딕스,radix?action=highlight&value=radix_sort]]
merge
comb
https://everything2.com/title/comb+sort
spaghetti
comb
shear
zen
https://everything2.com/title/Zen+Sort
random / bogo / stupid /
https://everything2.com/title/random+sort
== algorithm ==
== stable vs unstable ==
https://everything2.com/title/stable+sort
= sort / sorting / 정렬 #sort =
(대충 생각나는대로,chk) { [[키,key]]를 기준으로(primary_key 말고 secondary_key ...도 있는 경우가 있는데 tbw) , [[비교,comparison]]하여, (근데 Ggl:"비교정렬" 이 아닌 경우도 있는데 tbw) [[순서,order]]에 따라, 위치를 바꾸어서(교환, swap, exchange) }
=정렬,sorting =,sorting =,sort .
[[정렬,jeongryeol]] =정렬,sorting =,sorting =,sort .
sort WtEn:sort#Noun
sorting WtEn:sorting#Noun
소팅
Sub:
[[sort_명령]]
[[sort_명령]]?
----
정렬알고리즘을 분류하는 방법은 매우 다양한데
안정적인 정렬 vs 불안정 정렬
Naver:"안정적인 정렬 vs 불안정 정렬" Bing:"안정적인 정렬 vs 불안정 정렬" Ggl:"안정적인 정렬 vs 불안정 정렬"
안정:
불안정: quicksort
정렬알고리듬의 분류와 밀접:
[[시간복잡도,time_complexity]] <- 특히 가장 중요 주제.
[[공간복잡도,space_complexity]] - 일부에서.
----
radix
[[radix_sort]] ... curr at [[래딕스,radix?action=highlight&value=radix_sort]]
'''radix sort'''
Ggl:"radix sort"
merge
'''merge sort'''
https://everything2.com/title/Merge+SortGgl:"merge sort"
comb
https://everything2.com/title/comb+sort
Ggl:"comb sort"
spaghetti
Ggl:"spaghetti sort"
shear
Ggl:"shear sort"
quick - quicksort quick_sort
quick
quicksort quick_sort =,quicksort =,quick_sort ... WtEn:quicksort
Ggl:"quick sort"
REL
[[pivot]] - [[피벗,pivot]]
불안정정렬
[[시간복잡도,time_complexity]] \Theta(n\log n) O(n^2)
zen
https://everything2.com/title/Zen+Sort
Ggl:"zen sort"
random / bogo / stupid /
https://everything2.com/title/random+sort
Ggl:"random bogo stupid sort"
== stable vs unstable ==
https://everything2.com/title/stable+sort
@@ -1415,7 +1455,7 @@
= tmp 1 =
tmp/ written by dr j. lee, https://cafe.naver.com/kpope/931
$F=-\nabla U$ 이고 $ma=m\ddot{x}=\frac{d}{dt} [m\dot{x}]$ 입니다.
그런데 $m\dot{x}=\frac{\partial}{\partial \dot{x}} \frac{1}{2}m\dot{x}^2$
@@ -1424,9 +1464,78 @@
potential energy $V$ 가 오직 $x$ dependent (물론 velocity independent potential 에서)(
그러니
$F=ma$ 는 Euler-Lagrange equation과 equivalent합니다.
$\left[ \frac{\partial}{\partial x}-\frac{d}{dt}\frac{\partial}{\partial\dot{x}}\right](T-V)$
문제는 이것이 least-action principle로부터 유도되는 이유가 key입니다.
당시 Euler는 brachistochrone 문제들을 통해 이미 최소값과 관련한 calculus of variation 을 개발해 놓았고
이것이 이렇게 응용되어 결국 Hamilton's least-action principle로 완성되게 됩니다.
그러니
$F=ma$ 는 Euler-Lagrange equation과 equivalent합니다.
당시 Euler는 brachistochrone 문제들을 통해 이미 최소값과 관련한 calculus of variation 을 개발해 놓았고
이것이 이렇게 응용되어 결국 Hamilton's least-action principle로 완성되게 됩니다.
= tmp2 =
2024-06-06
Prof. Michael Bronstein (CS, University of Oxford, DeepMind prof. -> https://www.cs.ox.ac.uk/news/1996-full.html ) delivered a lecture titled
''Geometric Deep Learning: From Euclid to Drug Design''
as part of the Hot Topics in Computing Series at CSAIL.
https://www.youtube.com/watch?v=MeJgxYfiaz8
1:07
He's very well known for dynamic graph CNNs for learning on point clouds. // [[dynamic_graph_CNN]] [[점구름,point_cloud]]
3:30
[[Hermann_Weyl]]: "Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection" // [[대칭성,symmetry]]
4:00
[[플라톤,Plato]] (~370 BC)의 [[Platonic_solid]] (플라톤 입체 or 플라톤 다면체 ... [[입체,solid]]) 언급
4:44
[[에우클레이데스,Euclid]] (~300 BC)의 5th postulate, and 19세기에 나타난 비유클리드 언급
entire zoo of different geometries
* Euclidean
* affine
* projective
Euclidean_geometry [[유클리드_기하학,Euclidean_geometry]]
affine_geometry [[아핀기하학,affine_geometry]]
projective_geometry [[사영기하학,projective_geometry]]
이런 상황에서 '기하학을 어떻게 정의할 것인가'의 문제가 제기. (어떤 기하학이 다른 것보다 일반적인가?)
paradigm shift는 젊은 [[Felix_Klein]] (1872) { 23세에 독일 Erlangen 대학교 교수. }로부터 왔는데
그는 radically new way of thinking of geometry in terms of invariances 를 제안하였다. // [[불변성,invariance]]
geometric object를 group of transformations // 기하학적 [[대상,object]]: [[군,group]] of [[변환,transformation]]
-> [[Erlangen_program]]. WpKo:에를랑겐_프로그램 WpEn:Erlangen_program {Topics: [[동차공간,homogeneous_space]] }
6:00
ex.
Euclidean geometry
E(3)
https://i.imgur.com/TAZCDGI.png
[[Emmy_Noether]]: [[뇌터_정리,Noether_theorem]]: principles of symmetry에서 [[보존법칙,conservation_law]]을 도출할 수 있음을 보였음.
like: conservation of energy comes from symmetry of time.
([[에너지,energy]] 보존은 [[시간,time]] 대칭에서)
이것이 나중에 발전하여 [[입자물리학,particle_physics]]의 [[standard_model]].
6:56
물리에선 external vs internal symmetry를 구분
external symmetries of the spacetime - what is called the [[푸앵카레_군,Poincare_group]], that gives rise to the [[
external symmetry - R^^1,3^^ O(1,3) ...
internal symmetry - U(1) SU(2) SU(3) ...
7:30
"It is only slightly overstating the case to say that Physics is the study of symmetry" - P. Anderson // [[대칭성,symmetry]]
그럼 이게 ML([[기계학습,machine_learning]])과 무슨 관련인가?
We have historically different architectures of [[신경망,neural_network]]s such as
GNN
CNN
RNN
DeepSets
[[트랜스포머,transformer]]
...
다른 context에서 온 다른 architecture이다.
우린 여기서 [[공통분모,common_denominator]]를 찾고 싶다. (이미 있던 것들을) 설명하고, 같은 원리에 기반해 새로운 architecture를 설계(design)하는 걸 하고 싶은데, 이게 바로 GNN이다.
cont 8m
Contents
- 1. 메타 meta #meta
- 2. infinitive #infinitive 부정사 ?
- 3. geometry 기하 #geom
- 3.1. taxicab???
- 3.2. digital geometry
- 3.3. discrete geometry and combinatorial geometry
- 3.4. computational geometry
- 3.5. finite geometry
- 3.6. descriptive geometry
- 3.7. projective geometry
- 3.8. Euclidean geometry #euclidgeom
- 3.9. non-Euclidean geometry
- 3.10. absolute geometry
- 3.11. hyperbolic geometry
- 3.12. affine geometry
- 3.13. // rel. parallel_postulate
- 3.14. 리만 기하학
- 3.15. 정보기하학 information geometry
- 4. lock / locking
- 5. envelope
- 6. count / counting / counter + countability #count
- 7. allocator #allocator
- 8. 암호학 cryptology cryptography
- 9. context
- 10. expansion
- 11. transfer #transfer
- 12. generator #generator
- 13. sort / sorting / 정렬 #sort
- 14. fork / forking #fork
- 15. branch / branching #branch
- 16. (tmp, 위 두 sections.) fork vs branch
- 17. vertex #vertex
- 18. edge #edge
- 19. ambiguity
- 20. law / rule /
- 21. dual / duality
- 22. (시간 관련) past - (present) - future / priori posteriori / a priori a posteriori
- 23. 분해 decomposition
- 24. statistics
- 25. prediction / forecasting
- 26. meaning
- 27. closure #closure
- 28. 동기화,synchronization
- 29. denotation and connotation
- 30. natural language
- 31. 처리 processing
- 32. NLP
- 33. hidden Markov model HMM
- 34. Markov model
- 35. Intel_x86
- 36. disk
- 37. cone
- 38. mimetex version
- 39. referer test
- 40. gnuplot test
- 41. etc
- 42. TeX의 그리스 문자
- 43. orphaned pages
- 44. 이상익
- 45. Pagename Normalization
- 46. tmp 1
- 47. tmp2
1. 메타 meta #meta ¶
Sub:
metadata - 메타데이터,metadata or 메타자료,metadata ....
metadata
metadata
{
metaprogramming
메타프로그래밍
metadata - 메타데이터,metadata or 메타자료,metadata ....
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
p TheMetadata
metaobject metaobject =,metaobject . metaobject{
metaobject
객체,object or 대상,object?
MKL metaobject_protocol(MOP)
metaobject
https://en.wikipedia.org/wiki/Metaobject
} // metaobject
metaobject
metaobject
metaobject
metaobject
메타오브젝트
메타프로그래밍,metaprogramming =메타프로그래밍,metaprogramming =,metaprogramming . 메타프로그래밍 metaprogramming - 프로그래밍,programmingmetaobject
객체,object or 대상,object?
MKL metaobject_protocol(MOP)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://en.wikipedia.org/wiki/Metaobject
} // metaobject
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
{
metaprogramming
메타프로그래밍
https://en.wikipedia.org/wiki/Metaprogramming
} // metaprogramming
metaprogramming
metaprogramming
metaprogramming
메타프로그래밍
메타프로그래밍
메타이론,metatheory
메타정리,metatheorem
메타언어,metalanguage
{
} // metaprogramming
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
메타이론,metatheory
메타정리,metatheorem
메타언어,metalanguage
{
see also 논리학,logic#s-1.1
wk:
(Recall: 일단 '언어'는 '대상을 서술하는 것')
메타언어는 언어 그 자체를 서술/언급하는 언어나 심벌,symbol(기호,symbol).
고차언어라고도 한다. higher-order language ? higher-order language = metalanguage ?
Are higher-order language and metalanguage the same?
Are higher-order language and metalanguage the same?
메타언어의 문장,sentence이나 절,clause의 구조는 메타문법(
메타문법
메타문법
metasyntax ?
metagrammar ? ) 으로 기술,description된다.
'대상언어'가 있을 때 그 위에 그걸 서술하는 '메타언어'가 있는 것이다. (그래서 위에 aka high-order라고 한 것? chk)
(Recall: 일단 '언어'는 '대상을 서술하는 것')
메타언어는 언어 그 자체를 서술/언급하는 언어나 심벌,symbol(기호,symbol).
고차언어라고도 한다. higher-order language ? higher-order language = metalanguage ?
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
'대상언어'가 있을 때 그 위에 그걸 서술하는 '메타언어'가 있는 것이다. (그래서 위에 aka high-order라고 한 것? chk)
https://ko.wikipedia.org/wiki/메타_언어
} // metalanguage
메타수학,metamathematics =메타수학,metamathematics =,metamathematics 메타수학 metamathematics
{
https://ko.wikipedia.org/wiki/메타수학
https://en.wikipedia.org/wiki/Metamathematics
https://ja.wikipedia.org/wiki/超数学
} // metalanguage
메타수학,metamathematics =메타수학,metamathematics =,metamathematics 메타수학 metamathematics
{
https://ko.wikipedia.org/wiki/메타수학
https://en.wikipedia.org/wiki/Metamathematics
https://ja.wikipedia.org/wiki/超数学
...
메타수학
} // metamathematics
metagraph 메타그래프,graph ? - 그래프,graph?
metaclass 메타클래스,metaclass? - 클래스,class - curr at 클래스%2Cclass?action=highlight&value=meta#s-2.3
metasyntax - 다른 syntax를 기술,description하기 위한 syntax였나? chk - curr at 신택스,syntax?action=highlight&value=metasyntax
metasyntactic_variable - 이게 이름이 foo bar 그런거였는데... metasyntax와 비슷한, 이런 이름이 붙은 이유? 다른 프로그램(실질적으로 쓰일 어떤 프로그램)의 코드의 예시를 보여주기 위해, 즉 template? 실질적으로는 의미가 없는 그런 variable
metalogic =,metalogic =,metalogic . metalogic
{
metalogic
메타논리
메타논리학
중에?
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
} // metamathematics
metagraph 메타그래프,graph ? - 그래프,graph?
metaclass 메타클래스,metaclass? - 클래스,class - curr at 클래스%2Cclass?action=highlight&value=meta#s-2.3
metasyntax - 다른 syntax를 기술,description하기 위한 syntax였나? chk - curr at 신택스,syntax?action=highlight&value=metasyntax
metasyntactic_variable - 이게 이름이 foo bar 그런거였는데... metasyntax와 비슷한, 이런 이름이 붙은 이유? 다른 프로그램(실질적으로 쓰일 어떤 프로그램)의 코드의 예시를 보여주기 위해, 즉 template? 실질적으로는 의미가 없는 그런 variable
metalogic =,metalogic =,metalogic . metalogic
{
metalogic
메타논리
메타논리학
중에?
rel formation_rule =,formation_rule =,formation_rule . formation_rule { formation rule
formation_rule
Formation_rule = https://en.wikipedia.org/wiki/Formation_rule ... "formation rule
formation rule
formation rule }
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
https://ko.wikipedia.org/wiki/메타논리학
https://simple.wikipedia.org/wiki/Metalogic
https://en.wikipedia.org/wiki/Metalogic
https://ja.wikipedia.org/wiki/メタ論理学
https://simple.wikipedia.org/wiki/Metalogic
https://en.wikipedia.org/wiki/Metalogic
https://ja.wikipedia.org/wiki/メタ論理学
Sub:
metalogic_programming =,metalogic_programming =,metalogic_programming . metalogic_programming
}
metalogic_programming =,metalogic_programming =,metalogic_programming . metalogic_programming
}
2.1. infinitive form 부정형 ? ¶
infinitive form
infinitive_form =,infinitive_form . infinitive_form
"infinitive form"
infinitive form
infinitive form
infinitive form
infinitive_form =,infinitive_form . infinitive_form
"infinitive form"
![NdEn: NdEn:](/wiki/imgs/interwiki/nden-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
2.2. infinitive verb ¶
infinitive verb
"infinitive verb"
infinitive_verb =,infinitive_verb . infinitive_verb
infinitive_verb
infinitive_verb
"infinitive verb"
infinitive_verb =,infinitive_verb . infinitive_verb
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpSp: WpSp:](/wiki/imgs/interwiki/wpsp-16.png)
3.1. taxicab??? ¶
taxicab_geometry =,taxicab_geometry =,taxicab_geometry . taxicab_geometry
{
taxicab geometry
(del or rename ok)
taxicab_geometry
MKL 거리,distance 노름,norm 그리드,grid 래티스,lattice 격자,lattice
taxicab geometry
taxicab geometry
"taxicab geometry"
}
{
taxicab geometry
(del or rename ok)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
MKL 거리,distance 노름,norm 그리드,grid 래티스,lattice 격자,lattice
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"taxicab geometry"
}
3.2. digital geometry ¶
https://en.wikipedia.org/wiki/Digital_geometry
digital geometry
digital geometry
digital geometry
"digital geometry"
}
mentions
https://en.wikipedia.org/wiki/Bresenham's_line_algorithm
digital_topology =,digital_topology =,digital_topology . digital_topology {
digital_topology https://en.wikipedia.org/wiki/Digital_topology }
digital_manifold =,digital_manifold =,digital_manifold . digital_manifold {
digital_manifold
Digital_manifold = https://en.wikipedia.org/wiki/Digital_manifold }
digital_topology =,digital_topology =,digital_topology . digital_topology {
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
digital_manifold =,digital_manifold =,digital_manifold . digital_manifold {
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"digital geometry"
}
3.3. discrete geometry and combinatorial geometry ¶
discrete_geometry =,discrete_geometry =,discrete_geometry . discrete_geometry
combinatorial_geometry =,combinatorial_geometry =,combinatorial_geometry . combinatorial_geometry
{
discrete geometry and combinatorial geometry
discrete geometry
combinatorial geometry
combinatorial_geometry =,combinatorial_geometry =,combinatorial_geometry . combinatorial_geometry
{
discrete geometry and combinatorial geometry
discrete geometry
combinatorial geometry
https://en.wikipedia.org/wiki/Discrete_geometry
"combinatorial geometry"
}
"Discrete geometry and combinatorial geometry are"
"discrete geometry""combinatorial geometry"
}
3.4. computational geometry ¶
computational geometry
computational_geometry =,computational_geometry =,computational_geometry . computational_geometry
{
computational geometry
계산기하
계산기하학
computational_geometry =,computational_geometry =,computational_geometry . computational_geometry
{
computational geometry
계산기하
계산기하학
https://ko.wikipedia.org/wiki/계산기하학
Computational_geometry = https://en.wikipedia.org/wiki/Computational_geometry
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
3.5. finite geometry ¶
finite geometry
finite_geometry =,finite_geometry =,finite_geometry . finite_geometry
finite_geometry
https://en.wikipedia.org/wiki/Finite_geometry
finite geometry
finite geometry
finite geometry
"finite geometry"
finite_geometry =,finite_geometry =,finite_geometry . finite_geometry
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://en.wikipedia.org/wiki/Finite_geometry
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"finite geometry"
finite_mathematics = discrete_mathematics 와 관계?? 근데 geometry에선 finite_geometry ≠ discrete_geometry ??
3.6. descriptive geometry ¶
descriptive_geometry =,descriptive_geometry =,descriptive_geometry . descriptive_geometry
{
descriptive geometry
descriptive_geometry
https://en.wikipedia.org/wiki/Descriptive_geometry
"descriptive geometry"
}
{
descriptive geometry
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://en.wikipedia.org/wiki/Descriptive_geometry
"descriptive geometry"
}
기술
서술 ....??
서술 ....??
3.7. projective geometry ¶
projective_geometry =,projective_geometry =,projective_geometry . projective_geometry
projective_geometry
{
projective geometry
projective geometry
projective_geometry
https://en.wikipedia.org/wiki/Projective_geometry
사영,projection
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
{
projective geometry
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://en.wikipedia.org/wiki/Projective_geometry
사영,projection
3.8. Euclidean geometry #euclidgeom ¶
Euclidean_geometry =,Euclidean_geometry =,Euclidean_geometry . Euclidean_geometry
{
Euclidean geometry
Euclidean_geometry
https://ko.wikipedia.org/wiki/유클리드_기하학
https://en.wiktionary.org/wiki/Euclidean_geometry
Euclidean_geometry = https://en.wikipedia.org/wiki/Euclidean_geometry
유클리드 기하학 = https://namu.wiki/w/유클리드 기하학
{
Euclidean geometry
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://ko.wikipedia.org/wiki/유클리드_기하학
https://en.wiktionary.org/wiki/Euclidean_geometry
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Namu: Namu:](/wiki/imgs/interwiki/namu-16.png)
"Euclidean geometry"
Euclidean geometry
Euclidean geometry
"Euclidean geometry"
"Euclidean geometry"
}
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"Euclidean geometry"
"Euclidean geometry"
}
3.9. non-Euclidean geometry ¶
non-Euclidean_geometry =,non-Euclidean_geometry =,non-Euclidean_geometry . non-Euclidean_geometry
{
비유클리드_기하학
non-Euclidean geometry
noneuclidean_geometry =,noneuclidean_geometry // https://en.wiktionary.org/wiki/noneuclidean_geometry <- US spelling
https://en.wiktionary.org/wiki/non-Euclidean_geometry
https://ko.wikipedia.org/wiki/비유클리드_기하학
https://simple.wikipedia.org/wiki/Non-Euclidean_geometry
https://en.wikipedia.org/wiki/Non-Euclidean_geometry
{
비유클리드_기하학
non-Euclidean geometry
noneuclidean_geometry =,noneuclidean_geometry // https://en.wiktionary.org/wiki/noneuclidean_geometry <- US spelling
https://en.wiktionary.org/wiki/non-Euclidean_geometry
https://ko.wikipedia.org/wiki/비유클리드_기하학
https://simple.wikipedia.org/wiki/Non-Euclidean_geometry
https://en.wikipedia.org/wiki/Non-Euclidean_geometry
}
쌍곡기하학 hyperbolic geometry hyperbolic_geometry hyperbolic_geometry ..... hyperbolic_space ?
hyperbolic_space
타원기하학 elliptic geometry elliptic_geometry (aka elliptical_geometry ? chk) .... 타원 기하학이 적용되는 위상공간: 타원 공간(elliptic space) elliptic_space
elliptic_space
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
타원기하학 elliptic geometry elliptic_geometry (aka elliptical_geometry ? chk) .... 타원 기하학이 적용되는 위상공간: 타원 공간(elliptic space) elliptic_space
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
3.10. absolute geometry ¶
절대기하,absolute_geometry =,absolute_geometry . absolute_geometry
{
absolute geometry
absolute_geometry
https://ko.wikipedia.org/wiki/절대기하학
https://en.wikipedia.org/wiki/Absolute_geometry
"absolute geometry"
}
{
absolute geometry
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://ko.wikipedia.org/wiki/절대기하학
https://en.wikipedia.org/wiki/Absolute_geometry
"absolute geometry"
}
3.11. hyperbolic geometry ¶
hyperbolic_geometry =,hyperbolic_geometry =,hyperbolic_geometry . hyperbolic_geometry
{
hyperbolic geometry
쌍곡기하
hyperbolic_geometry
https://ko.wikipedia.org/wiki/쌍곡기하학
https://simple.wikipedia.org/wiki/Hyperbolic_geometry
https://en.wikipedia.org/wiki/Hyperbolic_geometry
hyperbolic geometry
hyperbolic geometry
"hyperbolic geometry"
"hyperbolic geometry"
"hyperbolic geometry"
"hyperbolic geometry"
}
{
hyperbolic geometry
쌍곡기하
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://ko.wikipedia.org/wiki/쌍곡기하학
https://simple.wikipedia.org/wiki/Hyperbolic_geometry
https://en.wikipedia.org/wiki/Hyperbolic_geometry
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"hyperbolic geometry"
"hyperbolic geometry"
"hyperbolic geometry"
"hyperbolic geometry"
}
3.12. affine geometry ¶
affine_geometry =,affine_geometry =,affine_geometry . affine_geometry
{
affine geometry
https://mathworld.wolfram.com/AffineGeometry.html
https://en.wiktionary.org/wiki/affine_geometry
https://everything2.com/title/affine geometry
Affine_geometry = https://en.wikipedia.org/wiki/Affine_geometry
affine geometry
affine geometry
"affine geometry"
"affine geometry"
}
{
affine geometry
https://mathworld.wolfram.com/AffineGeometry.html
https://en.wiktionary.org/wiki/affine_geometry
https://everything2.com/title/affine geometry
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"affine geometry"
"affine geometry"
}
3.14. 리만 기하학 ¶
리만 기하학(Riemannian geometry)
Riemannian geometry
Rel
리만_계량,Riemannian_metric =리만_계량,Riemannian_metric =,Riemannian_metric 리만_계량 Riemannian_metric { Riemannian metric "Riemannian metric"
Riemannian metric }
리만_계량,Riemannian_metric =리만_계량,Riemannian_metric =,Riemannian_metric 리만_계량 Riemannian_metric { Riemannian metric "Riemannian metric"
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
Twin
"리만 기하학"
리만 기하학
리만 기하학
"Riemannian geometry"
Riemannian geometry
Riemannian geometry
Riemannian geometry
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"Riemannian geometry"
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
4. lock / locking ¶
Sub:
=,deadlock . deadlock
{
deadlock
http://wiki.c2.com/?DeadLock
}
=,livelock . livelock
{
livelock
http://wiki.c2.com/?LiveLock
=,deadlock . deadlock
{
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
http://wiki.c2.com/?DeadLock
}
=,livelock . livelock
{
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
http://wiki.c2.com/?LiveLock
aka process_starvation ( Up: resource_starvation ? or just starvation ? )
}
lock-free_synchronization
lock-based_synchronization = pessimistic_locking
read write lock
http://wiki.c2.com/?ReadWriteLock
read write lock
}
lock-free_synchronization
lock-based_synchronization = pessimistic_locking
read write lock
http://wiki.c2.com/?ReadWriteLock
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
6. count / counting / counter + countability #count ¶
count
count
counting
counter
countability
v. 세다
adj. 역- 반대- 의 뜻도 있음 - counter emf, ccw, etc.
countingadj. 역- 반대- 의 뜻도 있음 - counter emf, ccw, etc.
세기
counter세는 변수
세는 기계 - 계수기 ,
countability세는 기계 - 계수기 ,
가산성
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
6.4. countability #countable ¶
countable adj.
countability n.
countability n.
Sub:
가산집합,countable_set =가산집합,countable_set =,countable_set 가산집합 countable_set (at local w)
countable_infinity - w
countable_additivity - w
가산공리 or 가산성공리 / countability_axiom or axiom_of_countability - w
가산집합,countable_set =가산집합,countable_set =,countable_set 가산집합 countable_set (at local w)
가산집합
셀수있는집합
countable_set
opp. 비가산집합,uncountable_set
countable set { countable set = 가산집합 = 셀수있는집합 VS. 셀수없는집합 = 비가산집합}
가산집합
countable_set
비가산집합,uncountable_set =비가산집합,uncountable_set 비가산집합,uncountable_set 비가산집합 uncountable_set셀수있는집합
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
opp. 비가산집합,uncountable_set
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
countable_infinity - w
countable_additivity - w
가산공리 or 가산성공리 / countability_axiom or axiom_of_countability - w
가산성,countability - w
7. allocator #allocator ¶
할당자,allocator ? 할당,allocation하는
=할당자,allocator =,allocator =,allocator . allocator
allocator = https://en.wiktionary.org/wiki/allocator (볼필요x easy)
allocator
allocator
allocator
=할당자,allocator =,allocator =,allocator . allocator
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
allocator
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
7.1. memory allocator ¶
메모리할당자,memory_allocator ? 메모리,memory를 할당,allocation하는 i.e. 메모리할당,memory_allocation하는
memory allocator
메모리할당자
메모리할당기
중에?
memory allocator
메모리할당자
메모리할당기
중에?
w l
https://en.wiktionary.org/wiki/memory_allocator x 2024-06
// memory allocator ....
memory allocator
memory allocator
memory allocator
memory_allocator
// memory allocator ....
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![NN: NN:](/wiki/imgs/interwiki/nn-16.png)
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
7.1.1. slab allocator ¶
slab_allocator =,slab_allocator . slab_allocator
slab_allocator
https://www.minzkn.com/moniwiki/wiki.php/SlabAllocator
slab allocator
slab allocator
"slab allocator"
slab_allocator
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://www.minzkn.com/moniwiki/wiki.php/SlabAllocator
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"slab allocator"
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
8. 암호학 cryptology cryptography ¶
=암호학, =,cryptology =,cryptography .
둘중에 pagename tbd
cryptology
cryptography
cryptology
cryptography
암호학,cryptology
암호학,cryptography
cryptology cryptography 차이
cryptology cryptography 차이
cryptology cryptography 차이
둘중에 pagename tbd
둘다 page 만들어서 역할을 나눌수도
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![NdEn: NdEn:](/wiki/imgs/interwiki/nden-16.png)
![NdEn: NdEn:](/wiki/imgs/interwiki/nden-16.png)
암호학,cryptology
암호학,cryptography
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
Intw:
암호학
https://simple.wikipedia.org/wiki/Cryptography
http://en.citizendium.org/wiki/Cryptography
https://en.wikipedia.org/wiki/Cryptography
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
https://simple.wikipedia.org/wiki/Cryptography
http://en.citizendium.org/wiki/Cryptography
https://en.wikipedia.org/wiki/Cryptography
9. context ¶
Sub:
맥락,context
문맥,context
실행맥락,execution_context - context is curr at there too
context_switching
....
맥락,context
문맥,context
실행맥락,execution_context - context is curr at there too
context_switching
....
context_sensitivity ?
context sensitivity
https://en.wikipedia.org/wiki/Context-sensitive
이 개념은 언어,language 문법,grammar 자동기계,automaton = 유한상태기계(fsm)에 나온다
https://en.wikipedia.org/wiki/Context-sensitive
이 개념은 언어,language 문법,grammar 자동기계,automaton = 유한상태기계(fsm)에 나온다
10. expansion ¶
=,expansion .
expansion
expansion
expansion
수학에선 전개. vg에 현재 expansi로 보면 두개:
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![NdEn: NdEn:](/wiki/imgs/interwiki/nden-16.png)
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
수학에선 전개. vg에 현재 expansi로 보면 두개:
이항전개,binomial_expansion
전개,expansion
페이지 있음전개,expansion
text_expansion
text_expansion
text expansion
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
brace_expansion
brace_expansion
Brace_expansion p BraceExpansion https://rosettacode.org/wiki/Brace_expansion
brace expansion
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
rel. pattern_matching
12. generator #generator ¶
generator =,generator . generator
생성기 생성기,generator
생성자
제너레이터
발전기
발생기 - 난수발생기
RNG random number generator 등 ...
...
rel. generation { 생성,generation or 세대
생성기 생성기,generator
생성자
제너레이터
발전기
발생기 - 난수발생기
RNG random number generator 등 ...
...
rel. generation { 생성,generation or 세대
....(etc, misc)
VG titles with "genera" at 2023-08-20
생성모형,generative_model
생성함수,generating_function
확률생성함수,probability_generating_function,PGF
VG titles with "genera" at 2023-08-20
생성모형,generative_model
생성함수,generating_function
확률생성함수,probability_generating_function,PGF
12.1. random number generator (RNG) ¶
random number generation
random number generator (RNG)
=,RNG .
random number generator (RNG)
=,RNG .
REL random_number
https://en.wikipedia.org/wiki/Random_number_generation
https://en.wikipedia.org/wiki/List_of_random_number_generators
random number generator
random number generator
random number generator
https://en.wikipedia.org/wiki/List_of_random_number_generators
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
rel. randomness_test { randomness test rel. cryptography https://en.wikipedia.org/wiki/Randomness_test
randomness test 테스트,test는 검정,test? 판정법,test? }
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
13. sort / sorting / 정렬 #sort ¶
(대충 생각나는대로,chk) { 키,key를 기준으로(primary_key 말고 secondary_key ...도 있는 경우가 있는데 tbw) , 비교,comparison하여, (근데
비교정렬 이 아닌 경우도 있는데 tbw) 순서,order에 따라, 위치를 바꾸어서(교환, swap, exchange) }
정렬,jeongryeol =정렬,sorting =,sorting =,sort .
sort
sort#Noun
sorting
sorting#Noun
소팅
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
정렬,jeongryeol =정렬,sorting =,sorting =,sort .
sort
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
sorting
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
소팅
정렬알고리즘을 분류하는 방법은 매우 다양한데
quick
quicksort quick_sort =,quicksort =,quick_sort ...
quicksort
quick sort
REL
pivot - 피벗,pivot
불안정정렬
시간복잡도,time_complexity \Theta(n\log n) O(n^2)
quicksort quick_sort =,quicksort =,quick_sort ...
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
REL
pivot - 피벗,pivot
불안정정렬
시간복잡도,time_complexity \Theta(n\log n) O(n^2)
14.1. fork (system call) ¶
system_call로서의 fork:
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
= https://en.wikipedia.org/wiki/Fork_(system_call)
= https://en.wikipedia.org/wiki/Fork_(system_call)
이것의 응용: fork_bomb
fork_bomb =,fork_bomb =,fork_bomb . fork_bomb
fork_bomb =,fork_bomb =,fork_bomb . fork_bomb
{
fork_bomb
https://ko.wikipedia.org/wiki/포크_폭탄
https://simple.wikipedia.org/wiki/Fork_bomb
https://en.wikipedia.org/wiki/Fork_bomb
fork bomb
fork bomb
"fork bomb"
"fork bomb"
}//fork bomb
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://ko.wikipedia.org/wiki/포크_폭탄
https://simple.wikipedia.org/wiki/Fork_bomb
https://en.wikipedia.org/wiki/Fork_bomb
DoS (denial_of_service) 공격,attack =,dos =,attack =,dos_attack . {
https://ko.wikipedia.org/wiki/서비스_거부_공격
https://simple.wikipedia.org/wiki/Denial-of-Service_attack
https://en.wikipedia.org/wiki/Denial-of-service_attack
},
resource_starvation =,resource_starvation =,resource_starvation . resource_starvation
{
https://ko.wikipedia.org/wiki/서비스_거부_공격
https://simple.wikipedia.org/wiki/Denial-of-Service_attack
https://en.wikipedia.org/wiki/Denial-of-service_attack
},
resource_starvation =,resource_starvation =,resource_starvation . resource_starvation
{
resource starvation
resource_starvation x 2023-08-25
Resource_starvation redir to
Starvation_(computer_science)
resource starvation
resource starvation
"resource starvation"
}![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"resource starvation"
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"fork bomb"
"fork bomb"
}//fork bomb
16. (tmp, 위 두 sections.) fork vs branch ¶
공통된 뜻은 분기 분리 갈라짐 ... split
반대는 합쳐짐
두 단어 모두 computing에서 많이 쓰이는데 usage 차이가 있는데 확실히 tbw incl. reliable src.
둘다 VCS에서 쓰이는데 vcs에 따라 word usage가 차이가 있을수 있지만 대체로: fork는 한 project 전체가 대상이고 branch는 개발 과정의 한 시점인 특정 작업상태에 대한..? fork를 한다고 하면 대체로 어떤 특정 시점에서 전체 data의 dump를 얻는 것 같던데.
fork는 POSIX system_call 의 하나(for 프로세스,process관리, process_management) / branch는 아님
branch는 CPU(프로세서,process)의 conditional_jump 와 동의어? chk
반대는 합쳐짐
두 단어 모두 computing에서 많이 쓰이는데 usage 차이가 있는데 확실히 tbw incl. reliable src.
둘다 VCS에서 쓰이는데 vcs에 따라 word usage가 차이가 있을수 있지만 대체로: fork는 한 project 전체가 대상이고 branch는 개발 과정의 한 시점인 특정 작업상태에 대한..? fork를 한다고 하면 대체로 어떤 특정 시점에서 전체 data의 dump를 얻는 것 같던데.
fork는 POSIX system_call 의 하나(for 프로세스,process관리, process_management) / branch는 아님
branch는 CPU(프로세서,process)의 conditional_jump 와 동의어? chk
fork가 대체로 더 큰 범위에서 쓰이는 듯? (dump처럼)
fork branch 차이
fork branch 차이
fork branch 차이
software project 전체를 복제해서 다른 길로 가겠다 / wiki에도 쓰임(데이터 전체를 복사해 새 위키를) / cryptocurrency 에도 쓰임.
...![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Naver: Naver:](/wiki/imgs/interwiki/naver-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
19. ambiguity ¶
=,ambiguity .
ambiguity
애매성
애매모호함
모호성
중의성 애매성 (wk)
...
ambiguity
애매성
애매모호함
모호성
중의성 애매성 (wk)
...
chk 나만의생각:
ambiguous_grammar - 문법,grammar
이것은 해석,interpretation의 가능성,possibility의 수(해석하는 경우,case의 수)(해석 가능한 경우의_수,number_of_cases)가 하나냐 둘 이상이냐에(ie 단수냐 복수냐에)관한 것??
Sub:ambiguous_grammar - 문법,grammar
23.1. nodal decomposition ¶
nodal_decomposition =,nodal_decomposition . nodal_decomposition
{
nodal decomposition
https://en.wikipedia.org/wiki/Nodal_decomposition
nodal decomposition
범주론,category_theory
}
{
nodal decomposition
https://en.wikipedia.org/wiki/Nodal_decomposition
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
범주론,category_theory
}
24.1. 확률론 ¶
=확률론,probability_theory =,probability_theory . 확률론 probability_theory
확률론
확률론
![KmsK: KmsK:](/wiki/imgs/interwiki/kmsk-16.png)
{ 2023-11-18 현재 3개
combinatorial probability 조합적 확률론
probability theory 확률론
stochastics 확률론 // stochastics ....
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
}
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpSp: WpSp:](/wiki/imgs/interwiki/wpsp-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
25. prediction / forecasting ¶
=,prediction =,forecasting =,forecast .
예상
예측
예보
....
예상
예측
예보
....
비슷,cmp,mklink: estimation =,estimation .
estimation
tenataive pagename 추정,estimation
(we) "Estimation (or estimating) is the 과정,process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable."
https://en.wikipedia.org/wiki/Estimation
Cmp: 추론,inference
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
tenataive pagename 추정,estimation
MKL 추정량,estimator ..
이것은 (대개) 완벽할 수 없으므로 approximation 의 일종인가? (we) "Estimation (or estimating) is the 과정,process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable."
https://en.wikipedia.org/wiki/Estimation
https://simple.wikipedia.org/wiki/Prediction
https://simple.wikipedia.org/wiki/Forecasting
https://simple.wikipedia.org/wiki/Forecasting
Forecasting n.
forecast v.
forecast v.
27. closure #closure ¶
관련표현:
closed (특히 prefix. closed_set etc. opp. open_ ... curr at 형용사,adjective?action=highlight&value=closed)
closing
closed (특히 prefix. closed_set etc. opp. open_ ... curr at 형용사,adjective?action=highlight&value=closed)
closing
Sub:
(나중에 logic과 topology의 closure를 나누어야? 아님 필요 없나?)
https://en.wikipedia.org/wiki/Transitive_closure
closure_relation - curr 관계,relation?action=highlight&value=closure_relation
(나중에 logic과 topology의 closure를 나누어야? 아님 필요 없나?)
https://en.wikipedia.org/wiki/Transitive_closure
rel. transitivity / transitive_relation
https://en.wikipedia.org/wiki/Deductive_closurerel deduction ( 연역,deduction ... )
https://en.wikipedia.org/wiki/Symmetric_closurerel. 대칭성,symmetry / smallest symmetric_relation
https://en.wikipedia.org/wiki/Reflexive_closuresmallest reflexive_relation
https://en.wikipedia.org/wiki/Closure_operatorclosure_relation - curr 관계,relation?action=highlight&value=closure_relation
28. 동기화,synchronization ¶
QQQ 동기화,synchronization 성질을 가졌다는 명사형은? 동기성 synchrony synchronism ?
Sub:
=,wait-free_synchronization =,wait-free_synchronization . wait-free_synchronization
=,wait-free_synchronization =,wait-free_synchronization . wait-free_synchronization
wait-free synchronization
http://wiki.c2.com/?WaitFreeSynchronization
wait-free synchronization
"wait-free synchronization"
=,lock-free_synchronization =,lock-free_synchronization . lock-free_synchronizationhttp://wiki.c2.com/?WaitFreeSynchronization
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"wait-free synchronization"
lock-free synchronization
http://wiki.c2.com/?LockFreeSynchronization
lock-free synchronization
"lock-free synchronization"
=,lock-based_synchronization =,lock-based_synchronization . lock-based_synchronizationhttp://wiki.c2.com/?LockFreeSynchronization
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"lock-free synchronization"
lock-based synchronization
http://wiki.c2.com/?LockBasedSynchronization
lock-based synchronization
"lock-based synchronization"
=,sychronization_strategy =,sychronization_strategy . sychronization_strategyhttp://wiki.c2.com/?LockBasedSynchronization
- aka pessimistic_locking
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"lock-based synchronization"
sychronization strategy
http://wiki.c2.com/?SynchronizationStrategies
전략,strategy
sychronization strategy
"sychronization strategy"
http://wiki.c2.com/?SynchronizationStrategies
전략,strategy
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"sychronization strategy"
29. denotation and connotation ¶
denotation
connotation
denotation
connotation
(영어사전)
denotation n.(단어를 통한) 지시, 명시적 의미
connotation n. 함축(된 의미)
connotation
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
(영어사전)
denotation n.(단어를 통한) 지시, 명시적 의미
connotation n. 함축(된 의미)
29.1.1. denotational semantics ¶
denotational_semantics =,denotational_semantics .
https://en.wikipedia.org/wiki/Denotational_semantics
https://en.wikipedia.org/wiki/Denotational_semantics
denotational_semantics_of_the_Actor_model
https://en.wikipedia.org/wiki/Denotational_semantics_of_the_Actor_model
https://en.wikipedia.org/wiki/Denotational_semantics_of_the_Actor_model
actor_model =,actor_model . actor_model {
https://en.wikipedia.org/wiki/Actor_model
actor_model
model
}
https://en.wikipedia.org/wiki/Actor_model
![Srch: Srch:](/wiki/imgs/interwiki/srch-16.png)
model
}
30. natural language ¶
Sub:
자연 언어 이해 natural language understanding
자연 언어 처리 NLP //바로아래
자연 언어 질의 natural language query // via https://terms.naver.com/entry.naver?docId=830352&cid=50376&categoryId=50376
자연 언어 생성 natural language generation //via https://terms.naver.com/entry.naver?docId=830348&cid=50376&categoryId=50376
Opp:
인공어
artificial language
constructued language
conlang
자연 언어 이해 natural language understanding
자연 언어 처리 NLP //바로아래
자연 언어 질의 natural language query // via https://terms.naver.com/entry.naver?docId=830352&cid=50376&categoryId=50376
자연 언어 생성 natural language generation //via https://terms.naver.com/entry.naver?docId=830348&cid=50376&categoryId=50376
Opp:
인공어
artificial language
constructued language
conlang
Up: 언어,language
31. 처리 processing ¶
Sub:
처리장치,processing_unit
처리장치,processing_unit
이때의 unit은 한국어로 단위(단위,unit)보단 장치로 번역한다. (장치,device)
줄여서 처리기,processor와 동의어?
중앙처리장치,central_processing_unit,CPU
텐서처리장치,tensor_processing_unit,TPU
물리처리장치
graphics_processing_unit
자연어처리,natural_language_processing,NLP줄여서 처리기,processor와 동의어?
중앙처리장치,central_processing_unit,CPU
텐서처리장치,tensor_processing_unit,TPU
물리처리장치
graphics_processing_unit
33. hidden Markov model HMM ¶
=,hidden_Markov_model =,HMM .
hidden_Markov_model
HMM
hidden Markov model
hidden_Markov_model
HMM
hidden Markov model
은닉 마르코프 모델|모형
![WpKo: WpKo:](/wiki/imgs/interwiki/wpko-16.png)
https://en.wikipedia.org/wiki/Hidden_Markov_model
Up: Markov_model
35. Intel_x86 ¶
=,x86 . x86 x86_architecture ?
GDT,global_descriptor_table
LDT,local_descriptor_table
TSS,task_state_segment 태스크,task
call_gate 호출 게이트 / 콜 게이트 호출,call ? 콜,call ? 게이트,gate
task_gate 태스크 게이트 태스크,task
paging - curr at 메모리,memory?action=highlight&value=paging
LDT,local_descriptor_table
TSS,task_state_segment 태스크,task
call_gate 호출 게이트 / 콜 게이트 호출,call ? 콜,call ? 게이트,gate
task_gate 태스크 게이트 태스크,task
paging - curr at 메모리,memory?action=highlight&value=paging
descriptor
하지만 LDT 0번 디스크립터는 valid entry.
서술자 기술자 or 디스크립터 ...?
null_descriptor =,null_descriptor . null_descriptor
null_descriptor
null descriptor
descriptor_table =,descriptor_table . descriptor_table
descriptor table
GDT의 0번 디스크립터는 unusable.null_descriptor =,null_descriptor . null_descriptor
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
null descriptor
descriptor_table =,descriptor_table . descriptor_table
descriptor table
하지만 LDT 0번 디스크립터는 valid entry.
rel. description
35.1.1. real mode ¶
36.1. disk geometry/addressing ¶
CHS cylinder_head_sector
LBA logical_block_addressing
LBA logical_block_addressing
partition
{
디스크 사이즈 제한
MBR partition table은 섹터가 512바이트일 때 블럭 주소 한계가 232라서 2 TiB 제한.
GPT는 섹터가 512바이트일 때 264라서 8 ZiB 제한.
(table)
type
GPT = GUID_partition_tabletype
{
디스크 사이즈 제한
MBR partition table은 섹터가 512바이트일 때 블럭 주소 한계가 232라서 2 TiB 제한.
GPT는 섹터가 512바이트일 때 264라서 8 ZiB 제한.
LBA 0 : protective MBR. (무엇?)
LBA 1 : GPT header
LBA 2 :
}
LBA 1 : GPT header
LBA 2 :
}
36.2. boot booting ¶
=,boot =,booting .
boot_manager
MBR master_boot_record
MBR master_boot_record
boot_image
rel. disk_image
boot_recordboot_sector
VBR volume_boot_record
{
AKA volume boot sector, partition boot record, partition boot sector
}
{
AKA volume boot sector, partition boot record, partition boot sector
}
EBR extended_boot_record
{
AKA EPBR(extended partition boot record)
}
{
AKA EPBR(extended partition boot record)
}
BPB BIOS_parameter_block
EBPB extended_BIOS_parameter_block
EBPB extended_BIOS_parameter_block
37.2. light cone ¶
light cone
null cone
light_cone =,light_cone . null_cone =,null_cone .
null cone
light_cone =,light_cone . null_cone =,null_cone .
"light cone (or "null cone")" ... 널,null
상대론 relativity
사건,event
시공간,spacetime =,spacetime . spacetime { spacetime 시공간 시공 (시간,time + 공간,space ?)...
spacetime Up: physics { RR 물리physics 있음. VG 물리학,physics 있음. 물리,physics는 어떨지? }//physics }//spacetime
causality
빛,light
... btw,
Null_cone redir to
Null_vector
rel![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
null_cone = isotropic_cone - rel. null_vector isotropic_vector [1]
pagename은 널벡터,null_vector ... 벡터공간,vector_space의 zero_element =,zero_element . zero_element { zero element : 영원 영원소 중에?
zero element says: "영원(소)" ....
zero_element
zero_element .... 영,zero 원소,element }인 영벡터,zero_vector와 다른 것.
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
상대론 relativity
사건,event
시공간,spacetime =,spacetime . spacetime { spacetime 시공간 시공 (시간,time + 공간,space ?)...
![KpsE: KpsE:](/wiki/imgs/interwiki/kpse-16.png)
causality
빛,light
(중요하지 않은건 ADDHERE ... 그렇지 않은건 위쪽에.)
41. etc ¶
discharging:
$\displaystyle q=q_0e^{-\frac{t}{RC}}$
$\displaystyle V=V_0e^{-\frac{t}{RC}}$
$\displaystyle q=q_0e^{-\frac{t}{RC}}$
$\displaystyle V=V_0e^{-\frac{t}{RC}}$
limits vs nolimits
$\displaystyle \limits\int_a^bf(x)dx$
$\displaystyle \nolimits\int_a^bf(x)dx$
$\displaystyle \limits\int_a^bf(x)dx$
$\displaystyle \nolimits\int_a^bf(x)dx$
$\displaystyle |\limits_a^b$
$\displaystyle |\nolimits_a^b$
$\displaystyle |\nolimits_a^b$
영인자만들기:
$\displaystyle \begin{pmatrix}a&a\\b&b\end{pmatrix}\begin{pmatrix}x&-y\\-x&y\end{pmatrix},\; \begin{pmatrix}1&1\\-1&-1\end{pmatrix}\begin{pmatrix}1&1\\-1&-1\end{pmatrix}$
영인자
$\displaystyle \begin{pmatrix}a&a\\b&b\end{pmatrix}\begin{pmatrix}x&-y\\-x&y\end{pmatrix},\; \begin{pmatrix}1&1\\-1&-1\end{pmatrix}\begin{pmatrix}1&1\\-1&-1\end{pmatrix}$
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
42. TeX의 그리스 문자 ¶
대문자 명칭 나열:
$\displaystyle \Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi \Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega$
소문자 명칭 나열:
$\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \omicron \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega$
$\displaystyle \Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi \Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega$
소문자 명칭 나열:
$\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi \omicron \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega$
TeX는 그리스 문자를 표현할 때 로마자와 모양이 같은 것을 재활용한다. 따라서 그리스 대문자 목록을 표현하려면
$\displaystyle A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega$
소문자 목록은
$\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega$
var- 소문자 목록은
$\displaystyle \epsilon-\varepsilon/\theta-\vartheta/\pi-\varpi/\rho-\varrho/\sigma-\varsigma/\phi-\varphi$
$\displaystyle A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega$
소문자 목록은
$\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega$
var- 소문자 목록은
$\displaystyle \epsilon-\varepsilon/\theta-\vartheta/\pi-\varpi/\rho-\varrho/\sigma-\varsigma/\phi-\varphi$
표준 (italic)
$\displaystyle ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789$
$\displaystyle A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi$
을 다음과 같이 다양하게 표현을 시도, 아래 렌더링에서 어떤 꼴이 표현 지원되거나 지원되지 않는 지 확인 가능
$\displaystyle ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789$
$\displaystyle A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi$
을 다음과 같이 다양하게 표현을 시도, 아래 렌더링에서 어떤 꼴이 표현 지원되거나 지원되지 않는 지 확인 가능
mathcal:
$\displaystyle \mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathcal{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
$\displaystyle \mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathcal{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
mathrm:
$\displaystyle \mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathrm{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
$\displaystyle \mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathrm{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
mathbb:
$\displaystyle \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathbb{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
$\displaystyle \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathbb{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
mathbf:
$\displaystyle \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathbf{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
$\displaystyle \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathbf{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
mathscr:
$\displaystyle \mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathscr{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
$\displaystyle \mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789}$
$\displaystyle \mathscr{A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega \alpha \beta \gamma \delta \epsilon \zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi \chi \psi \omega \varepsilon\vartheta\varpi\varrho\varsigma\varphi}$
mathsf, mathtt는 전혀 지원 안하는 듯
44. 이상익 ¶
VG: 정수론,number_theory
$\displaystyle A=B \cdot Q+R, \quad\quad 0 \le R < B$
에서$\displaystyle R=A-B\left\lfloor \frac{A}{B} \right\rfloor$
// rel : 모듈로,modulo > modulo_operation https://proofwiki.org/wiki/Definition:Modulo_Operation45.1. TBD 1 ¶
맨 뒤에 ,ABBR postfix suffix 관습은 유지할 것인가 말것인가
abbr만으로 충분하다면 그것만 쓸것인가 아님 말것인가
...TBD
abbr만으로 충분하다면 그것만 쓸것인가 아님 말것인가
...TBD
일단 입출력은 입출력,IO로 했는데 편의상
46. tmp 1 ¶
tmp/ written by dr j. lee, https://cafe.naver.com/kpope/931
라그랑지안,Lagrangian은 먼저 $\displaystyle F=ma$ 에서 바로 나옵니다.
$\displaystyle F=-\nabla U$ 이고 $\displaystyle ma=m\ddot{x}=\frac{d}{dt} [m\dot{x}]$ 입니다.
그런데 $\displaystyle m\dot{x}=\frac{\partial}{\partial \dot{x}} \frac{1}{2}m\dot{x}^2$
이므로 $\displaystyle m\dot{x}=\frac{\partial}{\partial \dot{x}} T$ 입니다.
Cartesian coordinate에서는 kinetic energy T가 오직 $\displaystyle \dot{x}$ dependent
potential energy $\displaystyle V$ 가 오직 $\displaystyle x$ dependent (물론 velocity independent potential 에서)(
그러니
$\displaystyle F=ma$ 는 Euler-Lagrange equation과 equivalent합니다.
$\displaystyle \left[ \frac{\partial}{\partial x}-\frac{d}{dt}\frac{\partial}{\partial\dot{x}}\right](T-V)$
문제는 이것이 least-action principle로부터 유도되는 이유가 key입니다.
당시 Euler는 brachistochrone 문제들을 통해 이미 최소값과 관련한 calculus of variation 을 개발해 놓았고
이것이 이렇게 응용되어 결국 Hamilton's least-action principle로 완성되게 됩니다.
$\displaystyle F=-\nabla U$ 이고 $\displaystyle ma=m\ddot{x}=\frac{d}{dt} [m\dot{x}]$ 입니다.
그런데 $\displaystyle m\dot{x}=\frac{\partial}{\partial \dot{x}} \frac{1}{2}m\dot{x}^2$
이므로 $\displaystyle m\dot{x}=\frac{\partial}{\partial \dot{x}} T$ 입니다.
Cartesian coordinate에서는 kinetic energy T가 오직 $\displaystyle \dot{x}$ dependent
potential energy $\displaystyle V$ 가 오직 $\displaystyle x$ dependent (물론 velocity independent potential 에서)(
그러니
$\displaystyle F=ma$ 는 Euler-Lagrange equation과 equivalent합니다.
당시 Euler는 brachistochrone 문제들을 통해 이미 최소값과 관련한 calculus of variation 을 개발해 놓았고
이것이 이렇게 응용되어 결국 Hamilton's least-action principle로 완성되게 됩니다.
47. tmp2 ¶
2024-06-06
Prof. Michael Bronstein (CS, University of Oxford, DeepMind prof. -> https://www.cs.ox.ac.uk/news/1996-full.html ) delivered a lecture titled
Geometric Deep Learning: From Euclid to Drug Design
as part of the Hot Topics in Computing Series at CSAIL.
Prof. Michael Bronstein (CS, University of Oxford, DeepMind prof. -> https://www.cs.ox.ac.uk/news/1996-full.html ) delivered a lecture titled
Geometric Deep Learning: From Euclid to Drug Design
as part of the Hot Topics in Computing Series at CSAIL.
1:07
He's very well known for dynamic graph CNNs for learning on point clouds. // dynamic_graph_CNN 점구름,point_cloud
He's very well known for dynamic graph CNNs for learning on point clouds. // dynamic_graph_CNN 점구름,point_cloud
3:30
Hermann_Weyl: "Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection" // 대칭성,symmetry
4:00
플라톤,Plato (~370 BC)의 Platonic_solid (플라톤 입체 or 플라톤 다면체 ... 입체,solid) 언급
4:44
에우클레이데스,Euclid (~300 BC)의 5th postulate, and 19세기에 나타난 비유클리드 언급
Hermann_Weyl: "Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection" // 대칭성,symmetry
4:00
플라톤,Plato (~370 BC)의 Platonic_solid (플라톤 입체 or 플라톤 다면체 ... 입체,solid) 언급
4:44
에우클레이데스,Euclid (~300 BC)의 5th postulate, and 19세기에 나타난 비유클리드 언급
entire zoo of different geometries
affine_geometry 아핀기하학,affine_geometry
projective_geometry 사영기하학,projective_geometry
- Euclidean
- affine
- projective
affine_geometry 아핀기하학,affine_geometry
projective_geometry 사영기하학,projective_geometry
이런 상황에서 '기하학을 어떻게 정의할 것인가'의 문제가 제기. (어떤 기하학이 다른 것보다 일반적인가?)
paradigm shift는 젊은 Felix_Klein (1872) { 23세에 독일 Erlangen 대학교 교수. }로부터 왔는데
그는 radically new way of thinking of geometry in terms of invariances 를 제안하였다. // 불변성,invariance
geometric object를 group of transformations // 기하학적 대상,object: 군,group of 변환,transformation
-> Erlangen_program.
에를랑겐_프로그램
Erlangen_program {Topics: 동차공간,homogeneous_space }
그는 radically new way of thinking of geometry in terms of invariances 를 제안하였다. // 불변성,invariance
geometric object를 group of transformations // 기하학적 대상,object: 군,group of 변환,transformation
-> Erlangen_program.
![WpKo: WpKo:](/wiki/imgs/interwiki/wpko-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
6:00
ex.
Euclidean geometry
E(3)
![https://i.imgur.com/TAZCDGI.png](https://i.imgur.com/TAZCDGI.png)
E(3)
![https://i.imgur.com/TAZCDGI.png](https://i.imgur.com/TAZCDGI.png)
Emmy_Noether: 뇌터_정리,Noether_theorem: principles of symmetry에서 보존법칙,conservation_law을 도출할 수 있음을 보였음.
like: conservation of energy comes from symmetry of time.
(에너지,energy 보존은 시간,time 대칭에서)
이것이 나중에 발전하여 입자물리학,particle_physics의 standard_model.
like: conservation of energy comes from symmetry of time.
(에너지,energy 보존은 시간,time 대칭에서)
이것이 나중에 발전하여 입자물리학,particle_physics의 standard_model.
6:56
물리에선 external vs internal symmetry를 구분
external symmetries of the spacetime - what is called the 푸앵카레_군,Poincare_group, that gives rise to the [[
external symmetry - R1,3 O(1,3) ...
internal symmetry - U(1) SU(2) SU(3) ...
물리에선 external vs internal symmetry를 구분
external symmetries of the spacetime - what is called the 푸앵카레_군,Poincare_group, that gives rise to the [[
external symmetry - R1,3 O(1,3) ...
internal symmetry - U(1) SU(2) SU(3) ...
7:30
"It is only slightly overstating the case to say that Physics is the study of symmetry" - P. Anderson // 대칭성,symmetry
"It is only slightly overstating the case to say that Physics is the study of symmetry" - P. Anderson // 대칭성,symmetry
그럼 이게 ML(기계학습,machine_learning)과 무슨 관련인가?
We have historically different architectures of 신경망,neural_networks such as
다른 context에서 온 다른 architecture이다.
우린 여기서 공통분모,common_denominator를 찾고 싶다. (이미 있던 것들을) 설명하고, 같은 원리에 기반해 새로운 architecture를 설계(design)하는 걸 하고 싶은데, 이게 바로 GNN이다.
We have historically different architectures of 신경망,neural_networks such as
다른 context에서 온 다른 architecture이다.
우린 여기서 공통분모,common_denominator를 찾고 싶다. (이미 있던 것들을) 설명하고, 같은 원리에 기반해 새로운 architecture를 설계(design)하는 걸 하고 싶은데, 이게 바로 GNN이다.
cont 8m
----