Revisiting evolutionary information filteringManolis Vavalis
This document summarizes a study that experimentally evaluated the use of evolutionary algorithms for adaptive information filtering. The researchers tested a basic genetic algorithm approach using a vector space model to represent user profiles and documents, and found that it did not improve filtering accuracy over a baseline approach and struggled with the high-dimensional representation. Initializing profiles based on relevant documents and incorporating learning led to better initial performance but not better than the baseline. The researchers concluded the genetic algorithm was not well-suited for the complex, dynamic problem of adaptive information filtering within a high-dimensional vector space.
This document discusses solving systems of linear equations. It explains that a general system of equations can be converted to triangular form and then solved using back-substitution. It also states that elementary row operations preserve the set of solutions to a system of equations. Examples of elementary row operations include exchanging rows, multiplying a row by a non-zero constant, and replacing one row with itself plus a constant multiple of another row.
Archaeology and cultural heritage application working groupManolis Vavalis
The document summarizes discussions from a meeting of the Archaeology & Cultural Heritage Application Working Group. It describes the members of the working group, highlights from their activities over two years including a thematic workshop. The workshop addressed challenges around 3D knowledge technologies for cultural heritage applications. Critical problems discussed included acquisition of 3D data, search and retrieval, documentation and visualization. Real-life scenarios presented included a virtual exhibition and automatic identification of 3D objects. Open issues concerned the need for specialized 3D knowledge management tools and methodologies to address challenges in managing, preserving and providing access to 3D cultural heritage content.
Revisiting evolutionary information filteringManolis Vavalis
This document summarizes a study that experimentally evaluated the use of evolutionary algorithms for adaptive information filtering. The researchers tested a basic genetic algorithm approach using a vector space model to represent user profiles and documents, and found that it did not improve filtering accuracy over a baseline approach and struggled with the high-dimensional representation. Initializing profiles based on relevant documents and incorporating learning led to better initial performance but not better than the baseline. The researchers concluded the genetic algorithm was not well-suited for the complex, dynamic problem of adaptive information filtering within a high-dimensional vector space.
This document discusses solving systems of linear equations. It explains that a general system of equations can be converted to triangular form and then solved using back-substitution. It also states that elementary row operations preserve the set of solutions to a system of equations. Examples of elementary row operations include exchanging rows, multiplying a row by a non-zero constant, and replacing one row with itself plus a constant multiple of another row.
Archaeology and cultural heritage application working groupManolis Vavalis
The document summarizes discussions from a meeting of the Archaeology & Cultural Heritage Application Working Group. It describes the members of the working group, highlights from their activities over two years including a thematic workshop. The workshop addressed challenges around 3D knowledge technologies for cultural heritage applications. Critical problems discussed included acquisition of 3D data, search and retrieval, documentation and visualization. Real-life scenarios presented included a virtual exhibition and automatic identification of 3D objects. Open issues concerned the need for specialized 3D knowledge management tools and methodologies to address challenges in managing, preserving and providing access to 3D cultural heritage content.
Este documento presenta los conceptos de la descomposición LU de una matriz cuadrada A. Explica que una matriz A puede descomponerse en el producto de una matriz triangular inferior L y una matriz triangular superior U. Muestra un ejemplo numérico paso a paso de cómo calcular la descomposición LU de una matriz dada A.
This document discusses JavaBeans and the Expression Language (EL) in Java Server Pages (JSP). It describes how JavaBeans are reusable Java components that follow conventions for properties and methods. The EL allows easier access to JavaBeans properties without scripting code. It provides implicit objects to access attributes, request parameters, cookies and context initialization parameters. The EL supports operators and functions for conditions and evaluations.
This document discusses custom tag development in JSP, including using the <jsp:include> and <c:import> tags, passing parameters to tags, using attribute directives, handling long tag attributes, locating tags, creating a tag handler, and the tag API.
A JSP page is converted into a servlet at runtime. The servlet handles requests and responses, and incorporates the HTML, scriptlets, expressions, and other elements from the JSP page. The JSP lifecycle involves the container using directives to create an HttpServlet subclass, import statements, declaration statements, and build a _jspService() method that combines all the elements and runs the page. Elements like scriptlets and expressions are executed within the servlet and output is sent to the response.
This document provides an introduction to technologies of the World Wide Web. It discusses the history and components of the web including the World Wide Web (WWW), web servers, browsers like Mosaic, and hypertext languages like HTML, XHTML and XML. It also covers topics like how to structure and style web pages using CSS, the hypertext transport protocol (HTTP), and homework assignments to get a WordPress site hosted.
Este documento presenta los conceptos de la descomposición LU de una matriz cuadrada A. Explica que una matriz A puede descomponerse en el producto de una matriz triangular inferior L y una matriz triangular superior U. Muestra un ejemplo numérico paso a paso de cómo calcular la descomposición LU de una matriz dada A.
This document discusses JavaBeans and the Expression Language (EL) in Java Server Pages (JSP). It describes how JavaBeans are reusable Java components that follow conventions for properties and methods. The EL allows easier access to JavaBeans properties without scripting code. It provides implicit objects to access attributes, request parameters, cookies and context initialization parameters. The EL supports operators and functions for conditions and evaluations.
This document discusses custom tag development in JSP, including using the <jsp:include> and <c:import> tags, passing parameters to tags, using attribute directives, handling long tag attributes, locating tags, creating a tag handler, and the tag API.
A JSP page is converted into a servlet at runtime. The servlet handles requests and responses, and incorporates the HTML, scriptlets, expressions, and other elements from the JSP page. The JSP lifecycle involves the container using directives to create an HttpServlet subclass, import statements, declaration statements, and build a _jspService() method that combines all the elements and runs the page. Elements like scriptlets and expressions are executed within the servlet and output is sent to the response.
This document provides an introduction to technologies of the World Wide Web. It discusses the history and components of the web including the World Wide Web (WWW), web servers, browsers like Mosaic, and hypertext languages like HTML, XHTML and XML. It also covers topics like how to structure and style web pages using CSS, the hypertext transport protocol (HTTP), and homework assignments to get a WordPress site hosted.
1. Exètash Proìdou
Grammik 'Algebra
Antistrofoi PÐnakec
Jewr mata kai Ask seic
Tm ma Hlektrolìgwn Mhqanik¸n kai Mhqanik¸n Upologist¸n
Panepist mio JessalÐac
17 OktwbrÐou 2014
2. Exètash Proìdou
Ginìmeno Pinˆkwn
Kˆje st lh tou ginomènou twn dÔo pinˆkwn A B isoÔtai me to
ginìmeno tou A me thn antÐstoiqh st lh tou B.
A¢
0
... B¾¿1
BB@
...
¢ ¢ ¢ B¾¿n
...
...
1
CCA
Æ
0
BB@ ...
...
A¢B¾¿1
¢ ¢ ¢ A¢B¾¿n
...
...
1
CCA
Kˆje gramm tou ginomènou twn dÔo pinˆkwn A B isoÔtai me to
ginìmeno thc antÐstoiqhc gramm c tou A epÐ ton B.
0
BBB@
¢ ¢ ¢ A°½1
¢ ¢ ¢
...
¢ ¢ ¢ A°½n
¢ ¢ ¢
1
CCCA
¢B Æ
0
BBB@
¢ ¢ ¢ A°½1
¢B ¢ ¢ ¢
...
¢ ¢ ¢ A°½n
¢B ¢ ¢ ¢
1
CCCA
3. Exètash Proìdou
Orismìc antistrìfou
O antÐstrofoc enìc pÐnaka A eÐnai ènac ˆlloc pÐnakac B tètoioc
¸ste
AB Æ BA Æ I
O antÐstrofoc sun jwc sumbolÐzetai me A¡1.
4. Exètash Proìdou
AntÐstrofoc tou antÐstrofou
Je¸rhma
O antÐstrofoc tou antÐstrofou enìc pÐnaka eÐnai o Ðdioc o
pÐnakac. Dhlad ³
A¡1
´¡1
ÆA
.
Apìdeixh.
5. Exètash Proìdou
AntÐstrofoc tou antÐstrofou
Je¸rhma
O antÐstrofoc tou antÐstrofou enìc pÐnaka eÐnai o Ðdioc o
pÐnakac. Dhlad ³
A¡1
´¡1
ÆA
.
Apìdeixh.
AA¡1 ÆA¡1AÆ I.
6. Exètash Proìdou
AntÐstrofoc ginomènou
Je¸rhma
O antÐstrofoc tou ginomènou dÔo pinˆkwn isoÔtai me to ginìmeno,
me antÐstrofh seirˆ, twn antistrìfwn touc.
7. Exètash Proìdou
AntÐstrofoc ginomènou
Je¸rhma
O antÐstrofoc tou ginomènou dÔo pinˆkwn isoÔtai me to ginìmeno,
me antÐstrofh seirˆ, twn antistrìfwn touc. Dhlad
(AB)¡1 Æ B¡1A¡1.
Apìdeixh.
8. Exètash Proìdou
AntÐstrofoc ginomènou
Je¸rhma
O antÐstrofoc tou ginomènou dÔo pinˆkwn isoÔtai me to ginìmeno,
me antÐstrofh seirˆ, twn antistrìfwn touc. Dhlad
(AB)¡1 Æ B¡1A¡1.
Apìdeixh.
³
B¡1A¡1
´
(AB) Æ B¡1
³
A¡1A
´
B Æ B¡1IB Æ B¡1B Æ I.
9. Exètash Proìdou
AntÐstrofoc ginomènou
Je¸rhma
O antÐstrofoc tou ginomènou dÔo pinˆkwn isoÔtai me to ginìmeno,
me antÐstrofh seirˆ, twn antistrìfwn touc. Dhlad
(AB)¡1 Æ B¡1A¡1.
Apìdeixh.
³
B¡1A¡1
´
(AB) Æ B¡1
³
A¡1A
´
B Æ B¡1IB Æ B¡1B Æ I.
(AB)
³
B¡1A¡1
´
ÆA
³
BB¡1
´
A¡1 Æ AIA¡1 ÆAA¡1 Æ I.
11. Exètash Proìdou
Monadikìthta antistrìfou
Je¸rhma
An upˆrqei o antÐstrofoc autìc eÐnai monadikìc.
Apìdeixh.
'Estw ìti upˆrqoun dÔo antÐstrofoi tou A o B kai o C. Tìte
B
12. Exètash Proìdou
Monadikìthta antistrìfou
Je¸rhma
An upˆrqei o antÐstrofoc autìc eÐnai monadikìc.
Apìdeixh.
'Estw ìti upˆrqoun dÔo antÐstrofoi tou A o B kai o C. Tìte
B Æ BI
13. Exètash Proìdou
Monadikìthta antistrìfou
Je¸rhma
An upˆrqei o antÐstrofoc autìc eÐnai monadikìc.
Apìdeixh.
'Estw ìti upˆrqoun dÔo antÐstrofoi tou A o B kai o C. Tìte
B Æ BI Æ B(AC)
14. Exètash Proìdou
Monadikìthta antistrìfou
Je¸rhma
An upˆrqei o antÐstrofoc autìc eÐnai monadikìc.
Apìdeixh.
'Estw ìti upˆrqoun dÔo antÐstrofoi tou A o B kai o C. Tìte
B Æ BI Æ B(AC) Æ (BA)C Æ
15. Exètash Proìdou
Monadikìthta antistrìfou
Je¸rhma
An upˆrqei o antÐstrofoc autìc eÐnai monadikìc.
Apìdeixh.
'Estw ìti upˆrqoun dÔo antÐstrofoi tou A o B kai o C. Tìte
B Æ BI Æ B(AC) Æ (BA)C Æ IC Æ C.
16. Exètash Proìdou
AntÐstrofoc kai lÔseic
Je¸rhma
An upˆrqei o antÐstrofoc enìc pÐnaka A tìte
Ï upˆrqei monadik lÔsh tou sust matoc Ax Æ b gia
opoiod pote b
17. Exètash Proìdou
AntÐstrofoc kai lÔseic
Je¸rhma
An upˆrqei o antÐstrofoc enìc pÐnaka A tìte
Ï upˆrqei monadik lÔsh tou sust matoc Ax Æ b gia
opoiod pote b
Ï kai h mình lÔsh tou omogenoÔc sust matoc eÐnai h mhdenik .
Apìdeixh.
Ax Æ b
18. Exètash Proìdou
AntÐstrofoc kai lÔseic
Je¸rhma
An upˆrqei o antÐstrofoc enìc pÐnaka A tìte
Ï upˆrqei monadik lÔsh tou sust matoc Ax Æ b gia
opoiod pote b
Ï kai h mình lÔsh tou omogenoÔc sust matoc eÐnai h mhdenik .
Apìdeixh.
Ax Æ b)A¡1Ax ÆA¡1b
19. Exètash Proìdou
AntÐstrofoc kai lÔseic
Je¸rhma
An upˆrqei o antÐstrofoc enìc pÐnaka A tìte
Ï upˆrqei monadik lÔsh tou sust matoc Ax Æ b gia
opoiod pote b
Ï kai h mình lÔsh tou omogenoÔc sust matoc eÐnai h mhdenik .
Apìdeixh.
Ax Æ b)A¡1Ax ÆA¡1b)x ÆA¡1b.
20. Exètash Proìdou
'Uparxh antistrìfou
Je¸rhma
O antÐstrofoc enìc pÐnaka A upˆrqei ann ìla ta odhgˆ stoiqeÐa
metˆ thn apaloif me od ghsh tou A eÐnai mh mhdenikˆ.
Apìdeixh.
Gia na upˆrqei prèpei na mporoÔme na upologÐsoume ìlec tic
st lec tou.
Prèpei dhlad ta sust mata Avj Æ ej gia j Æ 1,2, . . . ,n na èqoun
ìla lÔsh.
21. Exètash Proìdou
AntÐstrofoc trigwnikoÔ
Je¸rhma
O antÐstrofoc enìc ˆnw(kˆtw) trigwnikoÔ pÐnaka eÐnai
ˆnw(kˆtw) trigwnikìc pÐnakac.
Apìdeixh.
EÔkolh allˆ jèlei ton qrìno thc kai eÐnai baret .
24. Exètash Proìdou
'Askhsh
O antÐstrofoc tou pÐnaka
·
1 3
2 4
¸
eÐnai o
·
¡2 3
2
1 ¡1
2
¸
.
Poiˆ eÐnai h lÔsh tou sust matoc
2x1 Å4x2 Æ 2
x1 Å3x2 Æ 1
25. Exètash Proìdou
'Askhsh
O antÐstrofoc tou pÐnaka
·
1 3
2 4
¸
eÐnai o
·
¡2 3
2
1 ¡1
2
¸
.
Poiˆ eÐnai h lÔsh tou sust matoc
2x1 Å4x2 Æ 2
x1 Å3x2 Æ 1
A)
·
1 2
3 1
¸
B)
·
1
0
¸
G)
·
0
3
¸
D)
· 1
2 0
¡0 1
¸
26. Exètash Proìdou
'Askhsh
O antÐstrofoc tou pÐnaka
·
1 3
2 4
¸
eÐnai o
·
¡2 3
2
1 ¡1
2
¸
.
Poiˆ eÐnai h lÔsh tou sust matoc
2x1 Å4x2 Æ 2
x1 Å3x2 Æ 1
A)
·
1 2
3 1
¸
B)
·
1
0
¸
G)
·
0
3
¸
D)
· 1
2 0
¡0 1
¸
Dikaiolog ste thn apˆnths sac
27. Exètash Proìdou
'Askhsh
O antÐstrofoc tou pÐnaka
·
1 3
2 4
¸
eÐnai o
·
¡2 3
2
1 ¡1
2
¸
.
Poiˆ eÐnai h lÔsh tou sust matoc
2x1 Å4x2 Æ 2
x1 Å3x2 Æ 1
A)
·
1 2
3 1
¸
B)
·
1
0
¸
G)
·
0
3
¸
D)
· 1
2 0
¡0 1
¸
Dikaiolog ste thn apˆnths sac
Apˆnthsh: To sÔsthma se morf pinˆkwn
·
1 3
2 4
¸
x Æ
·
1
2
¸
ˆra
lÔsh eÐnai h B):
·
¡2 3
2
1 ¡1
2
¸·
1
2
¸
Æ
·
1
0
¸
28. Exètash Proìdou
'Askhsh
ApodeÐxte ìti gia kˆje antistrèyimo pÐnaka A gia kˆje
pragmatikì arijmì r6Æ 0 isqÔei
(rA)¡1 Æ
1
r
A¡1
29. Exètash Proìdou
'Askhsh
ApodeÐxte ìti gia kˆje antistrèyimo pÐnaka A gia kˆje
pragmatikì arijmì r6Æ 0 isqÔei
(rA)¡1 Æ
1
r
A¡1
(
1
r
A¡1)rA Æ (r(
1
r
A¡1))AÆA¡1AÆ I
30. Exètash Proìdou
'Askhsh
EÐnai o pÐnakac
AÆ
2
4
1 2 3
1 2 4
1 2 5
3
5
Antistrèyimoc?
A Nai.
B 'Oqi.
G 'Iswc.
D Ta èqw qamèna.
31. Exètash Proìdou
'Askhsh
EÐnai o pÐnakac
B Æ
2
4
3
5
1 1 1
2 2 2
3 4 5
antistrèyimoc?
A Nai.
B 'Oqi.
G 'Iswc.
32. Exètash Proìdou
'Askhsh
An gnwrÐzoume ìti to sÔsthma
2
4
1 1 1
2 ¡1 0
3 4 5
3
5x Æ
2
4
3
5
0
0
0
èqei san lÔsh mìnon thn x Æ~0 ti isqÔei gia to sÔsthma
2
4
1 1 1
2 ¡1 0
3 4 5
3
5x Æ
2
4
3
5?
¡1
7
¡3
33. Exètash Proìdou
'Askhsh
An gnwrÐzoume ìti to sÔsthma
2
4
1 1 1
2 ¡1 0
3 4 5
3
5x Æ
2
4
3
5
0
0
0
èqei san lÔsh mìnon thn x Æ~0 ti isqÔei gia to sÔsthma
2
4
1 1 1
2 ¡1 0
3 4 5
3
5x Æ
2
4
3
5?
¡1
7
¡3
A Upˆrqei toulˆqiston mÐa lÔsh x.
B Upˆrqei to polÔ mia lÔsh x.
G Kai ta dÔo apo ta parapˆnw
D TÐpote apo ta parapˆnw.
34. Exètash Proìdou
'Askhsh
H isìthta (AÅB)T ÆAT ÅBT isqÔei
A Gia kˆje zeÔgoc n£n pinˆkwn A kai B.
B Gia kanèna zeÔgoc n£n pinˆkwn A kai B.
G Gia merikˆ mìnon zeÔgh n£n pinˆkwn A kai B en¸ gia ˆlla
den isqÔei
35. Exètash Proìdou
'Askhsh
H isìthta (AÅB)¡1 ÆA¡1 ÅB¡1 isqÔei
A Gia kˆje zeÔgoc n£n antistrèyimwn pinˆkwn A kai B.
B Gia kanèna zeÔgoc n£n antistrèyimwn pinˆkwn A kai B.
G Gia merikˆ mìnon zeÔgh n£n antistrèyimwn pinˆkwn A kai B
en¸ gia ˆlla den isqÔei