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Title:

Some remarks on biequidimensionality of topological spaces and Noetherian schemes

Description:

There are many examples of the fact that dimension and codimension behave somewhat counterintuitively. In EGA it is stated that a topological space is equidimensional, equicodimensional and catenary if and only if every maximal chain of irreducible closed subsets has the same length. We construct examples that show that this is not even true for...

There are many examples of the fact that dimension and codimension behave somewhat counterintuitively. In EGA it is stated that a topological space is equidimensional, equicodimensional and catenary if and only if every maximal chain of irreducible closed subsets has the same length. We construct examples that show that this is not even true for the spectrum of a Noetherian ring. This gives rise to two notions of biequidimensionality, and we show how these relate to the dimension formula and the existence of a codimension function. ; Comment: 12 pages Minimize

Year of Publication:

2014-03-23

Document Type:

text

Subjects:

Mathematics - Commutative Algebra ; Mathematics - Algebraic Geometry ; 13C15 ; 13E05 ; 14A05 ; 14A25

Mathematics - Commutative Algebra ; Mathematics - Algebraic Geometry ; 13C15 ; 13E05 ; 14A05 ; 14A25 Minimize

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Title:

The space of Cohen-Macaulay curves

Description:

One can consider the Hilbert scheme as a natural compactification of the space of smooth projective curves with fixed Hilbert polynomial. Here we consider a different modular compactification, namely the functor CM parameterizing curves together with a finite map to $\mathbb{P}^n$ that is generically a closed immersion. We prove that CM is an al...

One can consider the Hilbert scheme as a natural compactification of the space of smooth projective curves with fixed Hilbert polynomial. Here we consider a different modular compactification, namely the functor CM parameterizing curves together with a finite map to $\mathbb{P}^n$ that is generically a closed immersion. We prove that CM is an algebraic space by contructing a scheme W and a representable, surjective and smooth map W -> CM. Moreover, we show that CM satisfies the valuative criterion for properness. ; Comment: 39 pages Minimize

Year of Publication:

2014-03-24

Document Type:

text

Subjects:

Mathematics - Algebraic Geometry ; 14H10 ; 14C05

Mathematics - Algebraic Geometry ; 14H10 ; 14C05 Minimize

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Title:

The Cohen-Macaulay space of twisted cubics

Description:

In this work, we describe the Cohen-Macaulay space CM of twisted cubics parameterizing curves $C$ together with a finite map $i: C \to \mathbb{P}^3$ that is generically a closed immersion and such that $C$ has Hilbert polynomial $p(t)=3t+1$ with respect to $i$. We show that CM is irreducible, smooth and birational to one component of the Hilbert...

In this work, we describe the Cohen-Macaulay space CM of twisted cubics parameterizing curves $C$ together with a finite map $i: C \to \mathbb{P}^3$ that is generically a closed immersion and such that $C$ has Hilbert polynomial $p(t)=3t+1$ with respect to $i$. We show that CM is irreducible, smooth and birational to one component of the Hilbert scheme of twisted cubics. ; Comment: 16 pages, 2 figures Minimize

Year of Publication:

2014-03-25

Document Type:

text

Subjects:

Mathematics - Algebraic Geometry ; 14H10 ; 14H50 ; 14C05

Mathematics - Algebraic Geometry ; 14H10 ; 14H50 ; 14C05 Minimize

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Title:

The space of Cohen-Macaulay curves

Description:

In this thesis we discuss a moduli space of projective curves with a map to a given projective space. The functor CM parametrizes curves, that is, Cohen-Macaulay schemes of pure dimension 1, together with a finite map to the projective space that is an isomorphism onto its image away from a finite set of closed points. We proof that CM is an alg...

In this thesis we discuss a moduli space of projective curves with a map to a given projective space. The functor CM parametrizes curves, that is, Cohen-Macaulay schemes of pure dimension 1, together with a finite map to the projective space that is an isomorphism onto its image away from a finite set of closed points. We proof that CM is an algebraic space by contructing a scheme W and a representable, surjective and smooth map from W to CM. ; QC 20120229 Minimize

Publisher:

KTH, Matematik (Avd.) ; Stockholm

Year of Publication:

2012

Document Type:

Licentiate thesis, monograph ; info:eu-repo/semantics/masterThesis ; text

Language:

eng

Rights:

info:eu-repo/semantics/openAccess

info:eu-repo/semantics/openAccess Minimize

Relations:

Trita-MAT. MA, 1401-2278 ; 2012:04

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Title:

The space of Cohen–Macaulay curves and related topics

Description:

The space of Cohen–Macaulay curves is a compactification of the space of curves that are embedded in a given projective space Pn. The idea is similar to that of the Hilbert scheme but instead of adding degenerated curves, one considers only curves without embedded or isolated points. However, the curves need not be embedded into the projective s...

The space of Cohen–Macaulay curves is a compactification of the space of curves that are embedded in a given projective space Pn. The idea is similar to that of the Hilbert scheme but instead of adding degenerated curves, one considers only curves without embedded or isolated points. However, the curves need not be embedded into the projective space. Instead, they come with a finite morphism to Pn that is generically a closed immersion. More precisely, the space CM of Cohen–Macaulay curves parameterizes flat families of pairs where is a curve without embedded or isolated points and is a finite morphism that is an isomorphism onto its image away from finitely many closed points and such that has Hilbert polynomial p(t) with respect to the map . In Paper A we show that the moduli functor CM is represented by a proper algebraic space. This is done by constructing a smooth, surjective cover and by verifying the valuative criterion for properness. Paper B studies the moduli space CM in the particular case n = 3 and p(t) = 3t + 1, that is, the Cohen–Macaulay space of twisted cubics. We de- scribe the points of CM and show that they are in bijection with the points on the 12-dimensional component H0 of the Hilbert scheme of twisted cu- bics. Knowing the points of CM, we can then show that the moduli space is irreducible, smooth and has dimension 12. Paper C concerns the notion of biequidimensionality of topological spaces and Noetherian schemes. In EGA it is claimed that a topological space X is equidimensional, equicodimensional and catenary if and only if all maximal chains of irreducible closed subsets in X have the same length. We construct examples of topological spaces and Noetherian schemes showing that the sec- ond property is strictly stronger. This gives rise to two different notions of biequidimensionality, and we show how they relate to the dimension formula and the existence of a codimension function. ; QC 20140404 Minimize

Publisher:

KTH, Matematik (Avd.) ; Stockholm

Year of Publication:

2014

Document Type:

Doctoral thesis, comprehensive summary ; info:eu-repo/semantics/doctoralThesis ; text

Language:

eng

DDC:

516 Geometry *(computed)*

Rights:

info:eu-repo/semantics/openAccess

info:eu-repo/semantics/openAccess Minimize

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TRITA-MAT-A ; 2014:03

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Title:

Über den Einfluss der Stimulation / Inhibition des Epidermal growth factor receptor auf karzinogen- induzierte DNA-Schäden in oropharyngealen Schleimhautzellen

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

2012-07-26

Document Type:

Dissertation ; NonPeerReviewed

Subjects:

Medizinische Fakultät

Medizinische Fakultät Minimize

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http://edoc.ub.uni-muenchen.de/14695/

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Title:

Learning interpretable models

Description:

Interpretability is an important, yet often neglected criterion when applying machine learning algorithms to real-world tasks. An understandable model enables the user to gain more knowledge from his data and to participate in the knowledge discovery process in a more detailed way. Hence, learning interpretable models is a challenging task, whos...

Interpretability is an important, yet often neglected criterion when applying machine learning algorithms to real-world tasks. An understandable model enables the user to gain more knowledge from his data and to participate in the knowledge discovery process in a more detailed way. Hence, learning interpretable models is a challenging task, whose complexity comes from the problems that interpretability is a fuzzy, subjective concept and human mental capabilities are in some ways astonishingly limited. At the same time, interpretability is a critical problem, because it is crucial for problems that cannot be solved purely automatically. The work presented in this thesis is structured along the three dimensions of understandability, accuracy, and efficiency. It contains contributions on the levels of the optimization of the interpretability of a learner with and without knowledge of its internals (white box and black box approach), the description of a models errors by local patterns and the improvement of global models with local models. Starting from an analysis of the requirements for and measures of interpretability in the context of knowledge discovery, diverse possible approaches of generating understandable models are investigated, with a particular focus on interpretable Support Vector Machines and local effects in the data. Problems of existing techniques and ad-hoc approaches to understandability optimization are analyzed and improved algorithms are developed. Minimize

Contributors:

Morik, Katharina ; Müller, Heinrich

Year of Publication:

2006-10-20

Document Type:

doc-type:Text ; doc-type:doctoralThesis

Language:

eng

Subjects:

ddc:004 ; Machine learning ; Data mining ; Classification ; Interpretability ; Local patterns ; Local models

ddc:004 ; Machine learning ; Data mining ; Classification ; Interpretability ; Local patterns ; Local models Minimize

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Title:

Distributed collaborative structuring

Description:

Making Inter- and Intranet resources available in a structured way is one of the most important and challenging problems today. An underlying structure allows users to search for information, documents or relationships without a clearly defined information need. While search and filtering technology is becoming more and more powerful, the develo...

Making Inter- and Intranet resources available in a structured way is one of the most important and challenging problems today. An underlying structure allows users to search for information, documents or relationships without a clearly defined information need. While search and filtering technology is becoming more and more powerful, the development of such explorative access methods lacks behind. This work is concerned with the development of large-scale data mining methods that allow to structure information spaces based on loosely coupled user annotations and navigation patterns. An essential challenge, that was not yet fully realized in this context, is heterogeneity. Different users and user groups often have different preferences and needs on how to access an information collection. While current Business Intelligence, Information Retrieval or Content Management solutions allow for a certain degree of personalization, these approaches are still very static. This considerably limits their applicability in heterogeneous environments. This work is based on a novel paradigm, called collaborative structuring. This term is chosen as a generalization to the term collaborative filtering. Instead of only filtering items, collaborative structuring allows users to organize information spaces in a loosely coupled way, based on patterns emerging through data mining. A first contribution of the work is to define the conceptual notion of collaborative structuring as combinatorial optimization problem and to put it into relation with existing research in the areas of data and web mining. As second contribution, highly scalable, distributed optimization strategies are proposed and analyzed. Finally, the proposed approaches are quantitatively evaluated against existing methods using several real-world data sets. Also, practical experience from two application areas is given, namely information access for heterogeneous expert communities and collaborative media organization. Minimize

Contributors:

Morik, Katharina ; Müller, Heinrich

Year of Publication:

2008-07-17

Document Type:

doc-type:Text ; doc-type:doctoralThesis

Language:

eng

Subjects:

ddc:004 ; Informatik ; Data mining

ddc:004 ; Informatik ; Data mining Minimize

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Title:

Eine Predigt || Bey dem Begrebnis || der Edlen vnnd . Ehrentugentsamen || Frawen Catharinae, gebornen von Hoym/ des . || Herrn Heinrichs von Bila/ beider Rechten Doctoris,|| auff Heigenrode vnd der Stapelburg/ Heubtmans zu || Merseburg vnd Heringen etc. eheligen haußfrawen/|| welche den 2. Iulij im Jahr . || 1596. zu Heigenrode . || entschlaffen/ vnd den 9. desselbi=||gen alda . || begraben/|| beneben || Einer Elegia vnd kurtzen Trostschrifft . || gehalten vnd geschrieben || Durch || Henricum Eckstormium M. Pfarherrn vnd Recto-||rem im Stifft Walckenrede.||

Publisher:

Lucius, Jakob d.Ä.

Year of Publication:

1596

Source:

Eckstorm, Heinrich Bilen, Katharina: Eine Predigt || Bey dem Begrebnis || der Edlen vnnd . Ehrentugentsamen || Frawen Catharinae, gebornen von Hoym/ des . || Herrn Heinrichs von Bila/ beider Rechten Doctoris,|| auff Heigenrode vnd der Stapelburg/ Heubtmans zu || Merseburg vnd Heringen etc. eheligen haußfrawen/|| welche den 2. Iulij im Jahr . || ...

Eckstorm, Heinrich Bilen, Katharina: Eine Predigt || Bey dem Begrebnis || der Edlen vnnd . Ehrentugentsamen || Frawen Catharinae, gebornen von Hoym/ des . || Herrn Heinrichs von Bila/ beider Rechten Doctoris,|| auff Heigenrode vnd der Stapelburg/ Heubtmans zu || Merseburg vnd Heringen etc. eheligen haußfrawen/|| welche den 2. Iulij im Jahr . || 1596. zu Heigenrode . || entschlaffen/ vnd den 9. desselbi=||gen alda . || begraben/|| beneben || Einer Elegia vnd kurtzen Trostschrifft . || gehalten vnd geschrieben || Durch || Henricum Eckstormium M. Pfarherrn vnd Recto-||rem im Stifft Walckenrede.||. Helmstedt Berlin 1596 Minimize

Document Type:

Monograph ; Text

Subjects:

Historische Drucke ; Theologie

Historische Drucke ; Theologie Minimize

Rights:

Open Access

Open Access Minimize

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Title:

Copine III interacts with ERBB2 and promotes tumor cell migration

Description:

Other ; Diss. Phil.-Nat. Univ. Basel, 2009. - Ref.: Jan Hofsteenge ; Korref.: G. Christofori, Nancy E, Hynes

Other ; Diss. Phil.-Nat. Univ. Basel, 2009. - Ref.: Jan Hofsteenge ; Korref.: G. Christofori, Nancy E, Hynes Minimize

Publisher:

Basel, [s.n.]

Year of Publication:

2009

Language:

eng

Rights:

Basel, [s.n.]

Basel, [s.n.] Minimize

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