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• 201.
Department of Applied Mathematics, State University of Yerevan, Yerevan, USSR.
Computing Center, Academy of Sciences, Armenian SSR, Yerevan, USSR.
Stable properties of graphs1991Inngår i: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 90, nr 2, s. 143-152Artikkel i tidsskrift (Fagfellevurdert)

Abstract For many properties P Bondy and ChvÃ¡tal (1976) have found sufficient conditions such that if a graph G + uv has property P then G itself has property P. In this paper we will give a generalization that will improve ten of these conditions.

Fulltekst (pdf)
Stable properties of graphs
• 202.
Department of Mathematics, Luleå University, Luleå, Sweden.
Institute for System Programming, Russian Academy of Sciences, Moscow, Russia.
On the number of partial Steiner systems2000Inngår i: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 8, nr 5, s. 347-352Artikkel i tidsskrift (Fagfellevurdert)

We give a simple proof of the result of Grable on the asymptotics of the number of partial Steiner systems S(t,k,m).

Fulltekst (pdf)
On the number of partial Steiner systems
• 203.
Department of Mathematics, University of Umeå, Umeå, Sweden / Department of Mathematical Cybernetics, Yerevan State University, Yerevan, Republic of Armenia.
Department of Mathematical Cybernetics, Yerevan State University, Yerevan, Republic of Armenia.
Some panconnected and pancyclic properties of graphs with a local ore-type condition1996Inngår i: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 12, nr 3, s. 209-219Artikkel i tidsskrift (Fagfellevurdert)

Asratian and Khachatrian proved that a connected graphG of order at least 3 is hamiltonian ifd(u) + d(v) ≥ |N(u) ∪ N(v) ∪ N(w)| for any pathuwv withuv ∉ E(G), whereN(x) is the neighborhood of a vertexx.

We prove that a graphG with this condition, which is not complete bipartite, has the following properties:

1. a) For each pair of verticesx, y with distanced(x, y) ≥ 3 and for each integern, d(x, y) ≤ n ≤ |V(G)| − 1, there is anx − y path of lengthn.
2. (b)For each edgee which does not lie on a triangle and for eachn, 4 ≤ n ≤ |V(G)|, there is a cycle of lengthn containinge.
3. (c)Each vertex ofG lies on a cycle of every length from 4 to |V(G)|.

This implies thatG is vertex pancyclic if and only if each vertex ofG lies on a triangle.

Fulltekst (pdf)
Some panconnected and pancyclic properties of graphs with a local ore-type condition
• 204.
Technical University of Darmstadt, Germany .
University of Münster, Germany . Linköpings universitet, Matematiska institutionen, Matematisk statistik. Linköpings universitet, Tekniska högskolan. St. Petersburg State University, Russia.
Persistence probabilities for a Bridge of an integrated simple random walk2014Inngår i: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 34, nr 1, s. 1-22Artikkel i tidsskrift (Fagfellevurdert)

We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability n(-1/2) to stay positive. This question is motivated by random polymer models and proves a conjecture by Caravenna and Deuschel.

• 205.
Université Paris-Sud 11, France.
Remarks on maximal regularity2011Inngår i: Parabolic Problems: The Herbert Amann Festschrift / [ed] Joachim Escher, Patrick Guidotti, Matthias Hieber, Piotr Mucha, Jan W. Prüss, Yoshihiro Shibata, Gieri Simonett, Christoph Walker, Wojciech Zajaczkowski, Springer, 2011, s. 45-56Kapittel i bok, del av antologi (Annet vitenskapelig)

We prove weighted estimates for the maximal regularity operator. Such estimates were motivated by boundary value problems. We take this opportunity to study a class of weak solutions to the abstract Cauchy problem. We also give  a new proof of maximal regularity for closed and maximal accretive operators following from Kato's inequality for fractional powers and almost orthogonality arguments.

• 206.
Université Paris-Sud.
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I2011Inngår i: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 184, nr 1, s. 47-115Artikkel i tidsskrift (Fagfellevurdert)

We develop new solvability methods for divergence form second order, real and complex, elliptic systems  above Lipschitz graphs, with $L_2$ boundary data.    The coefficients $A$ may depend on all variables, but are assumed to be close to coefficients $A_0$ that are independent of the coordinate transversal to the boundary, in the Carleson sense $\|A-A_0\|_C$ defined by Dahlberg.  We obtain a number of {\em a priori} estimates and boundary behaviour results under finiteness of $\|A-A_0\|_C$.  Our methods yield full characterization of weak solutions, whose gradients have $L_2$ estimates of a non-tangential maximal function or of the square function, via an integral representation acting on the conormal gradient, with a singular operator-valued kernel.   Also, the non-tangential maximal function of a weak solution is controlled in $L_2$ by the square function of its   gradient. This estimate is new for systems in such generality, and even for real non-symmetric equations in dimension $3$  or higher. The existence of a proof {\em a priori} to well-posedness, is also a new fact.  As corollaries, we obtain well-posedness of the Dirichlet, Neumann and Dirichlet regularity problems under   smallness of $\|A-A_0\|_C$ and well-posedness for $A_0$, improving earlier results for real symmetric equations.  Our methods build on an algebraic reduction to a first order system first made for coefficients $A_0$ by the two authors   and A. McIntosh in order to use functional calculus related to the Kato conjecture solution,   and the main analytic tool for coefficients $A$ is an operational calculus to prove weighted maximal regularity estimates.

• 207.
Département de Mathématiques d’Orsay, Université Paris-Sud et UMR 8628 du CNRS, Orsay Cedex, France.
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems, II2012Inngår i: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 5, nr 5, s. 983-1061Artikkel i tidsskrift (Fagfellevurdert)

We continue the development, by reduction to a first-order system for the conormal gradient, of L2a priori estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence-form second-order complex elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning a priori almost everywhere nontangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying a posteriori a separate work on bounded domains.

• 208.
Deparrment of Biological Sciences Heriot-Watt University.
Lab. of Microbiology University of Ghent. Dept. of mathematics University of Turku. Nokia Mobile Phones. Lab. of microbiology Univesrity of Ghent. Lab. of microbiology University of Ghent. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Matematisk statistik.
Sliding window discretization: A new method for multiple band matching of bacterial genotyping fingerprints2004Inngår i: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 66, nr 6, s. 1575-1596Artikkel i tidsskrift (Fagfellevurdert)

Microbiologists have traditionally applied hierarchical clustering algorithms as their mathematical tool of choice to unravel the taxonomic relationships between micro-organisms. However, the interpretation of such hierarchical classifications suffers from being subjective, in that a variety of ad hoc choices must be made during their construction. On the other hand, the application of more profound and objective mathematical methods - such as the minimization of stochastic complexity - for the classification of bacterial genotyping fingerprints data is hampered by the prerequisite that such methods only act upon vectorized data. In this paper we introduce a new method, coined sliding window discretization, for the transformation of genotypic fingerprint patterns into binary vector format. In the context of an extensive amplified fragment length polymorphism (AFLP) data set of 507 strains from the Vibrionaceae family that has previously been analysed, we demonstrate by comparison with a number of other discretization methods that this new discretization method results in minimal loss of the original information content captured in the banding patterns. Finally, we investigate the implications of the different discretization methods on the classification of bacterial genotyping fingerprints by minimization of stochastic complexity, as it is implemented in the BinClass software package for probabilistic clustering of binary vectors. The new taxonomic insights learned from the resulting classification of the AFLP patterns will prove the value of combining sliding window discretization with minimization of stochastic complexity, as an alternative classification algorithm for bacterial genotyping fingerprints.

• 209.
Iterative methods for solving a nonlinear boundary inverse problem in glaciology2009Inngår i: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, ISSN 0928-0219 , Vol. 17, nr 3, s. 239-258Artikkel i tidsskrift (Fagfellevurdert)

We address a Cauchy problem for a nonlinear elliptic PDE arising in glaciology. After recasting the Cauchy problem as an ill-posed operator equation, we prove (for values of a certain parameter allowing Hilbert space techniques) differentiability properties of the associated operator. We also suggest iterative methods which can be applied to solve the operator problem.

• 210.
Bråk, en betydelsefull utmaning i matematik: En kvantitativ studie i form av intervention inom bråk på gruppnivå, Tier 2 i matematik på introduktionsprogrammet2019Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave

Studien har utgått från en modell, Respons to Intervention (RTI) och syftet har varit att bidra med kunskap om interventioner och att undersöka om en intervention, RTI på Tier 2nivå, i matematik inom området bråk genom explicit undervisning, laborativt material och digitalt läromedel (Nomp) har effekt på elever i svårigheter i matematik (årskurs 9) på introduktionsprogrammet. Urvalet av elever byggde på ett övergripande matematiktest som alla elever (n=40) i fyra olika matematikklasser genomfört vid samma tillfälle på introduktionsprogrammet på en gymnasieskola. För denna kvantitativa studie har både en experimentgrupp och en kontrollgrupp använts. 9 elever genomförde ett interventionsprogram gällande bråk, med fokus på begreppslig förmåga och procedurförmåga under tre veckor. Kontrollgruppen erhöll ingen interventionsinsats inom bråk utan deltog i den ordinarie matematikundervisningen om bråk.   Studiens resultat bygger på vår insamlade data i form av medelvärden på gruppnivå från interventionsgruppen och kontrollgruppen, från elevernas resultat på förtest och eftertest och analyser av dessa som vi genomfört med hjälp av SPSS (ANOVA). I resultatet framkom att båda grupperna utvecklats men interventionsgruppen hade som helhet utvecklats och blivit signifikant bättre än kontrollgruppen. När det gällde begreppslig förmåga visade mätningarna på att interventionsgruppen hade blivit statiskt signifikant bättre än kontrollgruppen. Gällande procedurförmåga utvecklades båda grupperna och blev bättre, men mätningarna visade inte på någon signifikant skillnad mellan grupperna. Resultatet visade även på betydelsen av att fokusera på begreppslig förmåga och att använda sig av både konkret och abstrakt material, för att elever ska få djupare förståelse för området bråk, där användning av tallinjen underlättade för eleverna i interventionsgruppen att förstå att bråktals värde. Det är önskvärt med fler studier där äldre elever ingår då behovet är stort (många äldre elever befinner sig i matematiksvårigheter) och det finns få studier att ta del av.

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• 211.
Univ Toulouse Isae Supaero, France.
Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten. Middle East Tech Univ, Turkey. Univ Toulouse Isae Supaero, France.
A TIGHTER BAYESIAN CRAMER-RAO BOUND2019Inngår i: 2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2019, s. 5277-5281Konferansepaper (Fagfellevurdert)

It has been shown lately that any "standard" Bayesian lower bound (BLB) on the mean squared error (MSE) of the Weiss-Weinstein family (WWF) admits a "tighter" form which upper bounds the "standard" form. Applied to the Bayesian Cramer-Rao bound (BCRB), this result suggests to redefine the concept of efficient estimator relatively to the tighter form of the BCRB, an update supported by a noteworthy example. This paper lays the foundation to revisit some Bayesian estimation problems where the BCRB is not tight in the asymptotic region.

• 212.
Stockholms University.
Stockholms University. University of Seville. Stockholms University. Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
Pentagrams and Paradoxes2011Inngår i: FOUNDATIONS OF PHYSICS, ISSN 0015-9018, Vol. 41, nr 3, s. 414-423Artikkel i tidsskrift (Fagfellevurdert)

Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum "paradoxes", such as that of Hardy.

Fulltekst (pdf)
FULLTEXT01
• 213.
Linköpings universitet, Institutionen för beteendevetenskap och lärande, Pedagogik och didaktik. Linköpings universitet, Utbildningsvetenskap.
Linköpings universitet, Institutionen för beteendevetenskap och lärande, Pedagogik och didaktik. Linköpings universitet, Utbildningsvetenskap.
Läxans vara eller icke vara i matematikundervisningen.: Påverkas elevers prestation och motivation av matematikläxor?2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

Syftet med denna systematiska litteraturstudie har varit att se hur forskare ser på läxan i allmänhet och i synnerhet matematikläxan. Med ett fokus på vilka olika typer av läxor det finns både i allmänhet men även inom matematikämnet. Fokus har även legat på hur läxor i matematik påverkar elevers motivation och prestation i matematikämnet.  Studien består av tolv artiklar och rapporter som använts för att besvara frågeställningarna. Vi har fokuserat på studier gjorda på elever i årskurs 4-6, men har använt artiklar och rapporter som diskuterar andra årskurser om resultaten kunnat generaliseras till andra årskurser. Begrepp som använts har varit matematik, läxa, motivation och prestation.  Resultatet visar att det finns många typer av matematikläxor som har olika betydelse för elevers motivation och prestation. Forskarna är inte eniga om något enhetligt svar på om matematikläxor påverkar elevers motivation och prestationer inom matematik. Flertalet av forskarna ser dock positivt på matematikläxan och anser att den påverkar elevers prestation till det bättre. Inom motivation är forskarna överrens om att läxor påverkar elevers motivation, det råder dock skilda åsikter om läxorna påverkar elevers motivation positivt eller negativt.

Fulltekst (pdf)
Läxans vara eller icke vara i matematikundervisningen.
• 214.
Universitat Politècnica de Catalunya, Barcelona, Spain.
The University of Western Australia, Crawley, WA, Australia. The University of Western Australia, Crawley, WA, Australia. Universitat Rovira i Virgili, Tarragona, Spain.
An alternative way to generalise the pentagon2013Inngår i: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 21, nr 4, s. 163-179Artikkel i tidsskrift (Fagfellevurdert)

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.

• 215.
Implementering av programmering i matematik åk 7-9: En litteraturstudie om tre olika programmeringsspråks lämplighet i olika matematikområden2018Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave

Hösten 2018 inrättas det en ny version av läroplanen från 2011 med mer fokus på programmering. Syftet med denna litteraturstudie är att sammanställa forskningslitteraturens resultat om olika programmeringsspråks lämplighet för högstadiets matematikundervisning, samt lämpliga matematikområden. Frågeställningarna jämför tre programmeringsspråk med avseende på deras lämplighet och för- och nackdelar i matematikundervisningen. Programmeringsspråken, som jämförs, är Scratch, Python och VBA (Visual Basics of Application, programmering i Microsofts kalkylprogram Excel). Litteraturstudiens resultat visar att Scratch och Python anses vara lämpliga för nybörjare och är utvecklade för att de ska vara lätta att lära sig och förstå medan VBA är det programmeringsspråk som är utvecklat för att utföra matematiska beräkningar med.

Programmeringsspråken kan användas i matematikundervisningen på likvärdiga sätt och i de flesta matematikområdena beroende på elevernas kompetens och lärarens val av uppgifter och tillvägagångssätt. Vidare är det möjligt att eleverna kan bli mer motiverade till att lära sig matematik om de har tillgång till digitala hjälpmedel eller programmering inom matematikundervisningen

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• 216.
Är Python pyton?: Erfarenheter vid användning av programmering i matematikundervisning i grundskolans senaste år2019Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave

Hösten 2018 inrättades en reviderad läroplan för grundskolan och gymnasiet. Den största förändringen var att programmering har lagts till i matematik- och teknikämnena. Med detta kommer frågor om hur programmering ska användas i matematikundervisningen och samtidigt inte försämra elevernas kunskaper och resultat. I denna pilotstudie undersöks elever i årskurs 9 och deras kunskapsutveckling och attitydförändring när programmering används för att räkna på aritmetiska talföljder. För denna studie användes programmeringsspråket Python som är ett lämpligt nybörjarspråk i programmering. I resultatet finns det inte några större skillnader i kunskapsutvecklingen varken hos kontrollgruppen som endast fick grundläggande programmering, eller hos de andra klasserna som hade totalt 6 lektioner med programmering med matematisk inriktning. Det fanns inte heller några tydliga förändringar i elevernas attityd mot matematik och programmering.  I studiens slutsats belyses många förbättringar som kan göras för framtida studier samt hur verksamma lärare kan använda programmeringen i matematikundervisningen.

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• 217. Kjøp publikasjonen >>
Coherent functors and asymptotic properties2019Doktoravhandling, med artikler (Annet vitenskapelig)

In this thesis we study properties of the so called coherent functors. Coherent functors were first introduced by Auslander in 1966 in a general setting. Coherent functors have been used since then as powerful tools for different purposes: to describe infinitesimal deformation theory, to describe algebraicity of a stack or to study properties of Rees algebras.

In 1998, Hartshorne proved that half exact coherent functors over a discrete valuation ring 𝐴 are direct sums of the identity functor, Hom-functors of quotient modules of 𝐴 and tensor products of quotient modules of 𝐴. In our first article (Paper A), we obtain a similar characterization for half exact coherent functors over a much wider class of rings: Dedekind domains. This fact allows us to classify half exact coherent functors over Dedekind domains.

In our second article (Paper B), coherent functors over noetherian rings are considered. We study asymptotic properties of sets of prime ideals connected with coherent functors applied to artinian modules or finitely generated modules. Also considering quotient modules M /anM, where an is the nthpower of an ideal 𝑎, one obtains that the Betti and Bass numbers of the images under a coherent functor of the quotient modules above are polynomials in n for large n. Furthermore, the lengths of these image modules are polynomial in 𝑛, for large 𝑛, under the condition that the image modules have finite length.

1. Half–Exact Coherent Functors over PIDs and Dedekind Domains
Åpne denne publikasjonen i ny fane eller vindu >>Half–Exact Coherent Functors over PIDs and Dedekind Domains
2016 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
##### Abstract [en]

The focus of this thesis is to characterize half–exact coherent functors over principal ideal domains (PIDs) and Dedekind domains. Ever since they where discovered, coherent functors have been useful in the study of some mathematical objects. We aim to explore a little more about them in this thesis.

We first give here a review of the general categorical notions relevant to the characterization. We also review the functors Ext(M,−) and Tor(M,−)  on the category on A–modules, where A is a commutative ring and M is an A–module.

With the assumption that A is a commutative noetherian ring, we introduce coherent functors defined on the category of finitely generated A–modules. It is then shown in the paper that any half–exact coherent functor over a PID, and more generally over a Dedekind domain, arises from a complex of projective modules.

##### Serie
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1752
##### Identifikatorer
urn:nbn:se:liu:diva-128616 (URN)978-91-7685-750-2 (ISBN)
##### Presentation
2016-06-08, Nobel (BL32), B-huset, Campus Valla, Linköping, 15:15 (engelsk)
##### Veileder

The thesis serie title Linköping Studies in Science and Technology. Licentiate Thesis is incorrect. The correct title is Linköping Studies in Science and Technology. Thesis.

Tilgjengelig fra: 2016-05-25 Laget: 2016-05-25 Sist oppdatert: 2019-05-13bibliografisk kontrollert
2. Coherent functors and asymptotic stability
Åpne denne publikasjonen i ny fane eller vindu >>Coherent functors and asymptotic stability
2019 (engelsk)Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 522Artikkel i tidsskrift (Fagfellevurdert) Published
##### Abstract [en]

Asymptotic properties of high powers of an ideal related to a coherent functor F are investigated. It is shown that when N is an artinian module the sets of attached prime ideals Att(A) F(0 :(N) a(n)) are the same for n large enough. Also it is shown that for an artinian module N if the modules F(0 :(N) a(n)) have finite length and for a finitely generated module M if the modules F(M/a(n) M) have finite length, their lengths are given by polynomials in n, for large n. When A is local it is shown that, the Betti numbers beta(i)(F(M /a(n) M)) and the Bass numbers mu(i)(F(M / a(n) M)) are given by polynomials in n for large n. (C) 2018 Elsevier Inc. All rights reserved.

##### sted, utgiver, år, opplag, sider
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2019
##### Emneord
Asymptotic prime ideal; Coherent functor; Hilbert polynomial; Betti number; Bass number
##### Identifikatorer
urn:nbn:se:liu:diva-154529 (URN)10.1016/j.jalgebra.2018.11.035 (DOI)000457509500001 ()

Funding Agencies|ISP through EAUMP

Tilgjengelig fra: 2019-02-20 Laget: 2019-02-20 Sist oppdatert: 2019-05-13
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Coherent functors and asymptotic properties
Errata
presentationsbild
• 218.
Half-exact coherent functors over Dedekind domains2019Inngår i: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 18, nr 5, artikkel-id 1950099Artikkel i tidsskrift (Fagfellevurdert)

Let A be a principal ideal domain (PID) or more generally a Dedekind domain and let F be a coherent functor from the category of finitely generated A-modules to itself. We classify the half-exact coherent functors F. In particular, we show that if F is a half-exact coherent functor over a Dedekind domain A, then F is a direct sum of functors of the form Hom(A) (P,-), Hom(A) (A/p(s),-) and A/p(s) circle times -, where P is a finitely generated projective A-module, p a nonzero prime ideal in A and s amp;gt;= 1.

Fulltekst (pdf)
fulltext
• 219.
Half–Exact Coherent Functors over PIDs and Dedekind Domains2016Licentiatavhandling, med artikler (Annet vitenskapelig)

The focus of this thesis is to characterize half–exact coherent functors over principal ideal domains (PIDs) and Dedekind domains. Ever since they where discovered, coherent functors have been useful in the study of some mathematical objects. We aim to explore a little more about them in this thesis.

We first give here a review of the general categorical notions relevant to the characterization. We also review the functors Ext(M,−) and Tor(M,−)  on the category on A–modules, where A is a commutative ring and M is an A–module.

With the assumption that A is a commutative noetherian ring, we introduce coherent functors defined on the category of finitely generated A–modules. It is then shown in the paper that any half–exact coherent functor over a PID, and more generally over a Dedekind domain, arises from a complex of projective modules.

omslag
presentationsbild
• 220.
Univ Zambia, Zambia.
Coherent functors and asymptotic stability2019Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 522Artikkel i tidsskrift (Fagfellevurdert)

Asymptotic properties of high powers of an ideal related to a coherent functor F are investigated. It is shown that when N is an artinian module the sets of attached prime ideals Att(A) F(0 :(N) a(n)) are the same for n large enough. Also it is shown that for an artinian module N if the modules F(0 :(N) a(n)) have finite length and for a finitely generated module M if the modules F(M/a(n) M) have finite length, their lengths are given by polynomials in n, for large n. When A is local it is shown that, the Betti numbers beta(i)(F(M /a(n) M)) and the Bass numbers mu(i)(F(M / a(n) M)) are given by polynomials in n for large n. (C) 2018 Elsevier Inc. All rights reserved.

• 221.
University of Southern Denmark, Denmark.
Restricted cycle factors and arc-decompositions of digraphs2015Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 193, s. 80-93Artikkel i tidsskrift (Fagfellevurdert)

We study the complexity of finding 2-factors with various restrictions as well as edge-decompositions in (the underlying graphs of) digraphs. In particular we show that it is N P-complete to decide whether the underlying undirected graph of a digraph D has a 2-factor with cycles C-1, C-2, ..., C-k such that at least one of the cycles C-i is a directed cycle in D (while the others may violate the orientation back in D). This solves an open problem from J. Bang-Jensen et al., Vertex-disjoint directed and undirected cycles in general digraphs, JCT B 106 (2014), 1-14. Our other main result is that it is also N P-complete to decide whether a 2-edge-colored bipartite graph has two edge-disjoint perfect matchings such that one of these is monochromatic (while the other does not have to be). We also study the complexity of a number of related problems. In particular we prove that for every even k greater than= 2, the problem of deciding whether a bipartite digraph of girth k has a k-cycle-free cycle factor is N P-complete. Some of our reductions are based on connections to Latin squares and so-called avoidable arrays.

Fulltekst (pdf)
fulltext
• 222.
What makes an (audio)book popular?2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

Audiobook reading has traditionally been used for educational purposes but has in recent times grown into a popular alternative to the more traditional means of consuming literature. In order to differentiate themselves from other players in the market, but also provide their users enjoyable literature, several audiobook companies have lately directed their efforts on producing own content. Creating highly rated content is, however, no easy task and one reoccurring challenge is how to make a bestselling story. In an attempt to identify latent features shared by successful audiobooks and evaluate proposed methods for literary quantiﬁcation, this thesis employs an array of frameworks from the ﬁeld of Statistics, Machine Learning and Natural Language Processing on data and literature provided by Storytel - Sweden’s largest audiobook company.

We analyze and identify important features from a collection of 3077 Swedish books concerning their promotional and literary success. By considering features from the aspects Metadata, Theme, Plot, Style and Readability, we found that popular books are typically published as a book series, cover 1-3 central topics, write about, e.g., daughter-mother relationships and human closeness but that they also hold, on average, a higher proportion of verbs and a lower degree of short words. Despite successfully identifying these, but also other factors, we recognized that none of our models predicted “bestseller” adequately and that future work may desire to study additional factors, employ other models or even use different metrics to deﬁne and measure popularity.

From our evaluation of the literary quantiﬁcation methods, namely topic modeling and narrative approximation, we found that these methods are, in general, suitable for Swedish texts but that they require further improvement and experimentation to be successfully deployed for Swedish literature. For topic modeling, we recognized that the sole use of nouns provided more interpretable topics and that the inclusion of character names tended to pollute the topics. We also identiﬁed and discussed the possible problem of word inﬂections when modeling topics for more morphologically complex languages, and that additional preprocessing treatments such as word lemmatization or post-training text normalization may improve the quality and interpretability of topics. For the narrative approximation, we discovered that the method currently suffers from three shortcomings: (1) unreliable sentence segmentation, (2) unsatisfactory dictionary-based sentiment analysis and (3) the possible loss of sentiment information induced by translations. Despite only examining a handful of literary work, we further found that books written initially in Swedish had narratives that were more cross-language consistent compared to books written in English and then translated to Swedish.

Fulltekst (pdf)
what_makes_an_audiobook_popular
• 223.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
Malmö University, Malmö, Sweden. Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten. Heidelberg Collaboratory for Image Processing, Heidelberg University, Heidelberg, Germany.
Extension of p-Laplace Operator for Image Denoising2016Inngår i: 27th IFIP TC 7 Conference, CSMO 2015, Sophia Antipolis, France, June 29 - July 3, 2015, Revised Selected Papers / [ed] Bociu, Lorena; Désidéri, Jean-Antoine; Habbal, Abderrahmane, Springer, 2016, s. 107-116Kapittel i bok, del av antologi (Fagfellevurdert)

In this work we introduce a novel operator $$\displaystyle \varDelta _(p,q)$$ as an extended family of operators that generalize the p-Laplace operator. The operator is derived with an emphasis on image processing applications, and particularly, with a focus on image denoising applications. We propose a non-linear transition function, coupling p and q, which yields a non-linear filtering scheme analogous to adaptive spatially dependent total variation and linear filtering. Well-posedness of the final parabolic PDE is established via pertubation theory and connection to classical results in functional analysis. Numerical results demonstrates the applicability of the novel operator $$\displaystyle \varDelta _(p,q)$$ .

• 224.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Fysik, elektroteknik och matematik. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Fysik, elektroteknik och matematik. Linköpings universitet, Tekniska fakulteten. Orebro Univ, Sweden. Shenzhen MSU BIT Univ, Peoples R China; Beijing Inst Technol, Peoples R China.
Damped second order flow applied to image denoising2019Inngår i: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 84, nr 6, s. 1082-1111Artikkel i tidsskrift (Fagfellevurdert)

In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Stormer-Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF.

• 225.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för systemteknik, Datorseende. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
On Backward p(x)-Parabolic Equations for Image Enhancement2015Inngår i: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 36, nr 2, s. 147-168Artikkel i tidsskrift (Fagfellevurdert)

In this study, we investigate the backward p(x)-parabolic equation as a new methodology to enhance images. We propose a novel iterative regularization procedure for the backward p(x)-parabolic equation based on the nonlinear Landweber method for inverse problems. The proposed scheme can also be extended to the family of iterative regularization methods involving the nonlinear Landweber method. We also investigate the connection between the variable exponent p(x) in the proposed energy functional and the diffusivity function in the corresponding Euler-Lagrange equation. It is well known that the forward problems converges to a constant solution destroying the image. The purpose of the approach of the backward problems is twofold. First, solving the backward problem by a sequence of forward problems we obtain a smooth image which is denoised. Second, by choosing the initial data properly we try to reduce the blurriness of the image. The numerical results for denoising appear to give improvement over standard methods as shown by preliminary results.

• 226. Kjøp publikasjonen >>
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
Risk-Neutral and Physical Estimation of Equity Market Volatility2013Licentiatavhandling, med artikler (Annet vitenskapelig)

The overall purpose of the PhD project is to develop a framework for making optimal decisions on the equity derivatives markets. Making optimal decisions refers e.g. to how to optimally hedge an options portfolio or how to make optimal investments on the equity derivatives markets. The framework for making optimal decisions will be based on stochastic programming (SP) models, which means that it is necessary to generate high-quality scenarios of market prices at some future date as input to the models. This leads to a situation where the traditional methods, described in the literature, for modeling market prices do not provide scenarios of sufficiently high quality as input to the SP model. Thus, the main focus of this thesis is to develop methods that improve the estimation of option implied surfaces from a cross-section of observed option prices compared to the traditional methods described in the literature. The estimation is complicated by the fact that observed option prices contain a lot of noise and possibly also arbitrage. This means that in order to be able to estimate option implied surfaces which are free of arbitrage and of high quality, the noise in the input data has to be adequately handled by the estimation method.

The first two papers of this thesis develop a non-parametric optimization based framework for the estimation of high-quality arbitrage-free option implied surfaces. The first paper covers the estimation of the risk-neutral density (RND) surface and the second paper the local volatility surface. Both methods provide smooth and realistic surfaces for market data. Estimation of the RND is a convex optimization problem, but the result is sensitive to the parameter choice. When the local volatility is estimated the parameter choice is much easier but the optimization problem is non-convex, even though the algorithm does not seem to get stuck in local optima. The SP models used to make optimal decisions on the equity derivatives markets also need generated scenarios for the underlying stock prices or index levels as input. The third paper of this thesis deals with the estimation and evaluation of existing equity market models. The third paper gives preliminary results which show that, out of the compared models, a GARCH(1,1) model with Poisson jumps provides a better fit compared to more complex models with stochastic volatility for the Swedish OMXS30 index.

1. Non-parametric estimation of the option implied risk-neutral density surface
Åpne denne publikasjonen i ny fane eller vindu >>Non-parametric estimation of the option implied risk-neutral density surface
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
##### Abstract [en]

Accurate pricing of exotic or illiquid derivatives which is consistent with noisy market prices presents a major challenge. The pricing accuracy will crucially depend on using arbitrage free inputs to the pricing engine. This paper develops a general optimization based framework for estimation of the option implied risk-neutral density (RND), while satisfying no-arbitrage constraints. Our developed framework is a generalization of the RNDs implied by existing parametric models such as the Heston model. Thus, the method considers all types of realistic surfaces and is hence not constrained to a certain function class. When solving the problem the RND is discretized making it possible to use general purpose optimization algorithms. The approach leads to an optimization model where it is possible to formulate the constraints as linear constraints making the resulting optimization problem convex. We show that our method produces smooth local volatility surfaces that can be used for pricing and hedging of exotic derivatives. By perturbing input data with random errors we demonstrate that our method gives better results than the Heston model in terms of yielding stable RNDs.

##### Emneord
Risk-neutral density surface, Non-parametric estimation, Optimization, No-arbitrage constraints, Implied volatility surface, Local volatility
##### Identifikatorer
urn:nbn:se:liu:diva-94357 (URN)
Tilgjengelig fra: 2013-06-25 Laget: 2013-06-25 Sist oppdatert: 2013-06-26bibliografisk kontrollert
2. Non-parametric estimation of local variance surfaces
Åpne denne publikasjonen i ny fane eller vindu >>Non-parametric estimation of local variance surfaces
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
##### Abstract [en]

In this paper we develop a general optimization based framework for estimation of the option implied local variance surface. Given a specific level of consistency with observed market prices there exist an infinite number of possible surfaces. Instead of assuming shape constraints for the surface, as in many traditional methods, we seek the solution in the subset of realistic surfaces. We select local volatilities as variables in the optimization problem since it makes it easy to ensure absence of arbitrage, and realistic local volatilities imply realistic risk-neutral density- (RND), implied volatility- and price surfaces. The objective function combines a measure of consistency with market prices, and a weighted integral of the squared second derivatives of local volatility in the strike and the time-to-maturity direction. Derivatives prices in the optimization model are calculated efficiently with a finite difference scheme on a non-uniform grid. The framework has previously been successfully applied to the estimation of RND surfaces. Compared to when modeling the RND, it is for local volatility much easier to choose the parameters in the model. Modeling the RND produces a convex optimization problem which is not the case when modeling local volatility, but empirical tests indicate that the solution does not get stuck in local optima. We show that our method produces local volatility surfaces with very high quality and which are consistent with observed option quotes. Thus, unlike many methods described in the literature, our method does not produce a local volatility surface with irregular shape and many spikes or a non-smooth and multimodal RND for input data with a lot of noise.

##### Emneord
Local volatility surface; Non-parametric estimation; Optimization; No-arbitrage conditions
##### Identifikatorer
urn:nbn:se:liu:diva-94358 (URN)
Tilgjengelig fra: 2013-06-25 Laget: 2013-06-25 Sist oppdatert: 2013-06-26bibliografisk kontrollert
3. Statistical tests for selected equity market models
Åpne denne publikasjonen i ny fane eller vindu >>Statistical tests for selected equity market models
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
##### Abstract [en]

In this paper we evaluate which of four candidate equity market models that provide the best fit to observed closing data for the OMXS30 index from 30 September 1986 to 6 May 2013. The candidate models are two GARCH type models and two stochastic volatility models. The stochastic volatility models are estimated with the help of Markov Chain Monte Carlo methods. We provide the full derivations of the posterior distributions for the two stochastic volatility models, which to our knowledge have not been provided in the literature before. With the help of statistical tests we conclude that, out of the four candidate models, a GARCH model which includes jumps in the index level provides the best fit to the observed OMXS30 closing data.

##### Emneord
GARCH models, stochastic volatility models, Markov Chain Monte Carlo methods, statistical tests
##### Identifikatorer
urn:nbn:se:liu:diva-94359 (URN)
Tilgjengelig fra: 2013-06-25 Laget: 2013-06-25 Sist oppdatert: 2013-06-26bibliografisk kontrollert
Fulltekst (pdf)
Risk-Neutral and Physical Estimation of Equity Market Volatility
omslag
• 227.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
Statistical tests for selected equity market modelsManuskript (preprint) (Annet vitenskapelig)

In this paper we evaluate which of four candidate equity market models that provide the best fit to observed closing data for the OMXS30 index from 30 September 1986 to 6 May 2013. The candidate models are two GARCH type models and two stochastic volatility models. The stochastic volatility models are estimated with the help of Markov Chain Monte Carlo methods. We provide the full derivations of the posterior distributions for the two stochastic volatility models, which to our knowledge have not been provided in the literature before. With the help of statistical tests we conclude that, out of the four candidate models, a GARCH model which includes jumps in the index level provides the best fit to the observed OMXS30 closing data.

• 228.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska fakulteten.
Modeling and evaluation of the option book hedging problem using stochastic programming2016Inngår i: Quantitative finance (Print), ISSN 1469-7688, E-ISSN 1469-7696, Vol. 16, nr 2, s. 259-273Artikkel i tidsskrift (Fagfellevurdert)

Hedging of an option book in an incomplete market with transaction costs is an important problem in finance that many banks have to solve on a daily basis. In this paper, we develop a stochastic programming (SP) model for the hedging problem in a realistic setting, where all transactions take place at observed bid and ask prices. The SP model relies on a realistic modeling of the important risk factors for the application, the price of the underlying security and the volatility surface. The volatility surface is unobservable and must be estimated from a cross section of observed option quotes that contain noise and possibly arbitrage. In order to produce arbitrage-free volatility surfaces of high quality as input to the SP model, a novel non-parametric estimation method is used. The dimension of the volatility surface is infinite and in order to be able solve the problem numerically, we use discretization and principal component analysis to reduce the dimensions of the problem. Testing the model out-of-sample for options on the Swedish OMXS30 index, we show that the SP model is able to produce a hedge that has both a lower realized risk and cost compared with dynamic delta and delta-vega hedging strategies.

• 229.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
Non-parametric estimation of local variance surfacesManuskript (preprint) (Annet vitenskapelig)

In this paper we develop a general optimization based framework for estimation of the option implied local variance surface. Given a specific level of consistency with observed market prices there exist an infinite number of possible surfaces. Instead of assuming shape constraints for the surface, as in many traditional methods, we seek the solution in the subset of realistic surfaces. We select local volatilities as variables in the optimization problem since it makes it easy to ensure absence of arbitrage, and realistic local volatilities imply realistic risk-neutral density- (RND), implied volatility- and price surfaces. The objective function combines a measure of consistency with market prices, and a weighted integral of the squared second derivatives of local volatility in the strike and the time-to-maturity direction. Derivatives prices in the optimization model are calculated efficiently with a finite difference scheme on a non-uniform grid. The framework has previously been successfully applied to the estimation of RND surfaces. Compared to when modeling the RND, it is for local volatility much easier to choose the parameters in the model. Modeling the RND produces a convex optimization problem which is not the case when modeling local volatility, but empirical tests indicate that the solution does not get stuck in local optima. We show that our method produces local volatility surfaces with very high quality and which are consistent with observed option quotes. Thus, unlike many methods described in the literature, our method does not produce a local volatility surface with irregular shape and many spikes or a non-smooth and multimodal RND for input data with a lot of noise.

• 230.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
Non-parametric estimation of the option implied risk-neutral density surfaceManuskript (preprint) (Annet vitenskapelig)

Accurate pricing of exotic or illiquid derivatives which is consistent with noisy market prices presents a major challenge. The pricing accuracy will crucially depend on using arbitrage free inputs to the pricing engine. This paper develops a general optimization based framework for estimation of the option implied risk-neutral density (RND), while satisfying no-arbitrage constraints. Our developed framework is a generalization of the RNDs implied by existing parametric models such as the Heston model. Thus, the method considers all types of realistic surfaces and is hence not constrained to a certain function class. When solving the problem the RND is discretized making it possible to use general purpose optimization algorithms. The approach leads to an optimization model where it is possible to formulate the constraints as linear constraints making the resulting optimization problem convex. We show that our method produces smooth local volatility surfaces that can be used for pricing and hedging of exotic derivatives. By perturbing input data with random errors we demonstrate that our method gives better results than the Heston model in terms of yielding stable RNDs.

• 231.
University of Mediterranea Reggio Calabria, Italy.
University of Florence, Italy. Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. RUDN University, Russia.
Quasilinear elliptic equations on noncompact Riemannian manifolds2017Inngår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 273, nr 11, s. 3426-3462Artikkel i tidsskrift (Fagfellevurdert)

The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary value problems, with homogeneous Neumann conditions, in possibly irregular Euclidean domains are included as a special instance. A nontrivial solution is shown to exist under an unconventional growth condition on the right-hand side, which depends on the geometry of the underlying manifold. The identification of the critical growth is a crucial step in our analysis, and entails the use of the isocapacitary function of the manifold. A condition involving its isoperimetric function is also provided. (C) 2017 Elsevier Inc. All rights reserved.

• 232.
Department of Computer Science and Engineering, The Pennsylvania State University, USA.
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan. Department of Statistics, University of Bologna, Italy.
Editorial Material: 3rd Special issue on matrix computations and statistics2010Inngår i: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 54, nr 12, s. 3379-3380Artikkel i tidsskrift (Annet vitenskapelig)

n/a

• 233.
On Poicarés Uniformization Theorem2006Independent thesis Basic level (professional degree), 20 poäng / 30 hpOppgave

A compact Riemann surface can be realized as a quotient space $\mathcal{U}/\Gamma$, where $\mathcal{U}$ is the sphere $\Sigma$, the euclidian plane $\mathbb{C}$ or the hyperbolic plane $\mathcal{H}$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal{U}\rightarrow\mathcal{U}/\Gamma$.

For each $\Gamma$ acting on $\mathcal{H}$ we have a polygon $P$ such that $\mathcal{H}$ is tesselated by $P$ under the actions of the elements of $\Gamma$. On the other hand if $P$ is a hyperbolic polygon with a side pairing satisfying certain conditions, then the group $\Gamma$ generated by the side pairing is discrete and $P$ tesselates $\mathcal{H}$ under $\Gamma$.

Fulltekst (pdf)
FULLTEXT01
• 234. Kjøp publikasjonen >>
On the Branch Loci of Moduli Spaces of Riemann Surfaces2012Doktoravhandling, med artikler (Annet vitenskapelig)

The spaces of conformally equivalent Riemann surfaces, Mg where g ≥ 1, are not manifolds. However the spaces of the weaker Teichmüller equivalence, Tg are known to be manifolds. The Teichmüller space Tg is the universal covering of Mg and Mg is the quotient space by the action of the modular group. This gives Mg an orbifold structure with a branch locus Bg. The branch loci Bg can be identified with Riemann surfaces admitting non-trivial automorphisms for surfaces of genus g ≥ 3. In this thesis we consider the topological structure of Bg. We study the connectedness of the branch loci in general by considering families of isolated strata and we we establish that connectedness is a phenomenon for low genera. Further, we give the orbifold structure of the branch locus of surfaces of genus 4 and genus 5 in particular, by studying the equisymmetric stratification of the branch locus.

Paper 1. In this paper we show that the strata corresponding to actions of order 2 and 3 belong to the same connected component for arbitrary genera. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.

Paper 2. This paper contains a collection of results regarding components of the branch loci, some of them proved in detail in other papers. It is shown that for any integer d if p is a prime such that p > (d + 2)2, there there exist isolated strata of dimension d in the moduli space of Riemann surfaces of genus (d + 1)(p − 1)/2. It is also shown that if we consider Riemann surfaces as Klein surfaces, the branch loci are connected for every genera due to reflections.

Paper 3. Here we consider surfaces of genus 4 and 5. Here we study the automorphism groups of Riemann surfaces of genus 4 and 5 up to topological equivalence and determine the complete structure of the equisymmetric stratification of the branch locus.

Paper 4. In this paper we establish that the connectedness of the branch loci is a phenomenon for low genera. More precisely we prove that the only genera g where Bg is connected are g = 3, 4, 13, 17, 19, 59.

1. On the connectedness of the branch locus of the moduli space of Riemann surfaces
Åpne denne publikasjonen i ny fane eller vindu >>On the connectedness of the branch locus of the moduli space of Riemann surfaces
2010 (engelsk)Inngår i: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 104, nr 1, s. 81-86Artikkel i tidsskrift (Fagfellevurdert) Published
##### Abstract [en]

The moduli space M-g of compact Riemann surfaces of genus g has the structure of an orbifold and the set of singular points of such orbifold is the branch locus B-g. In this article we present some results related with the topology of B-g. We study the connectedness of B-g for g andlt;= 8, the existence of isolated equisymmetric strata in the branch loci and finally we stablish the connectedness of the branch locus of the moduli space of Riemann surfaces considered as Klein surfaces. We just sketch the proof of some of the results; complete proofs will be published elsewhere.

##### sted, utgiver, år, opplag, sider
REAL ACAD CIENCIAS EXACTAS FISICAS and NATURALES, CALLE VALVERDE 22, MADRID, 28004, SPAIN, 2010
##### Emneord
Riemann surface, moduli space, automorphism
##### Identifikatorer
urn:nbn:se:liu:diva-54848 (URN)10.5052/RACSAM.2010.08 (DOI)000276304700008 ()
Original Publication: Gabriel Bartolini, Antonio F Costa, Milagros Izquierdo and Ana M Porto, On the connectedness of the branch locus of the moduli space of Riemann surfaces, 2010, REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, (104), 1, 81-86. http://dx.doi.org/10.5052/RACSAM.2010.08 Copyright: Real Academia de Ciencias, Espana Tilgjengelig fra: 2010-04-16 Laget: 2010-04-16 Sist oppdatert: 2015-03-09
2. On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus
Åpne denne publikasjonen i ny fane eller vindu >>On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus
2012 (engelsk)Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, nr 1, s. 35-45Artikkel i tidsskrift (Fagfellevurdert) Published
##### Abstract [en]

Let be an integer and let , where denotes the moduli space of compact Riemann surfaces of genus . Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space, we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belong to the same connected component. We also prove the connectedness of for and with the exception of the isolated points given by Kulkarni.

##### sted, utgiver, år, opplag, sider
American Mathematical Society, 2012
##### Emneord
Moduli spaces, Teichmüller modular group, automorphism group
##### Identifikatorer
urn:nbn:se:liu:diva-73196 (URN)10.1090/S0002-9939-2011-10881-5 (DOI)000299596000004 ()
##### Forskningsfinansiär
Swedish Research Council, 621-2007-6240 Tilgjengelig fra: 2011-12-21 Laget: 2011-12-21 Sist oppdatert: 2018-09-01
3. On the Orbifold Structure of the Moduli Space of Riemann Surfaces of Genera Four and Five
Åpne denne publikasjonen i ny fane eller vindu >>On the Orbifold Structure of the Moduli Space of Riemann Surfaces of Genera Four and Five
2014 (engelsk)Inngår i: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 108, nr 2, s. 769-793Artikkel i tidsskrift (Fagfellevurdert) Published
##### Abstract [en]

The moduli space Mg, of compact Riemann surfaces of genus g has orbifold structure since Mg is the quotient space of the Tiechmüller space by the action of the mapping class group. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we find the orbifold structure of the moduli spaces of Riemann surfaces of genera 4 and 5.

##### sted, utgiver, år, opplag, sider
Springer, 2014
##### Identifikatorer
urn:nbn:se:liu:diva-78016 (URN)10.1007/s13398-013-0140-8 (DOI)000340875100032 ()
Tilgjengelig fra: 2012-06-04 Laget: 2012-06-04 Sist oppdatert: 2017-04-10bibliografisk kontrollert
4. On the connected branch loci of moduli spaces
Åpne denne publikasjonen i ny fane eller vindu >>On the connected branch loci of moduli spaces
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
##### Abstract [en]

The moduli space Mg of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of such orbifold is the branch locus Bg. In this article we show that Bg is connected exactly for genera three, four, thirteen, seventeen, nineteen and fitfynine by the use automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

##### Identifikatorer
urn:nbn:se:liu:diva-78018 (URN)
Tilgjengelig fra: 2012-06-04 Laget: 2012-06-04 Sist oppdatert: 2012-06-05bibliografisk kontrollert
Fulltekst (pdf)
On the Branch Loci of Moduli Spaces of Riemann Surfaces
omslag
• 235. Kjøp publikasjonen >>
On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera2009Licentiatavhandling, med artikler (Annet vitenskapelig)

Compact Riemann surfaces of genus greater than 1 can be realized as quotient spaces of the hyperbolic plane by the action of Fuchsian groups. The Teichmüller space is the set of all complex structures of Riemann surfaces and the moduli space the set of conformal equivalence classes of Riemann surfaces. For genus greater than two the branch locus of the covering of the moduli space by the Teichmüller space can be identified wi the set of Riemann surfaces admitting non-trivial automorphisms. Here we give the orbifold structure of the branch locus of surfaces of genus 5 by studying the equisymmetric stratification of the branch locus. This gives the orbifold structure of the moduli space.

We also show that the strata corresponding to surfaces with automorphisms of order 2 and 3 belong to the same connected component for every genus. Further we show that the branch locus is connected with the exception of one isolated point for genera 5 and 6, it is connected for genus 7 and it is connected with the exception of two isolated points for genus 8.

1. On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus
Åpne denne publikasjonen i ny fane eller vindu >>On the connectedness of the branch locus of the moduli space of Riemann surfaces of low genus
2012 (engelsk)Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, nr 1, s. 35-45Artikkel i tidsskrift (Fagfellevurdert) Published
##### Abstract [en]

Let be an integer and let , where denotes the moduli space of compact Riemann surfaces of genus . Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space, we prove that the subloci corresponding to Riemann surfaces with automorphism groups isomorphic to cyclic groups of order 2 and 3 belong to the same connected component. We also prove the connectedness of for and with the exception of the isolated points given by Kulkarni.

##### sted, utgiver, år, opplag, sider
American Mathematical Society, 2012
##### Emneord
Moduli spaces, Teichmüller modular group, automorphism group
##### Identifikatorer
urn:nbn:se:liu:diva-73196 (URN)10.1090/S0002-9939-2011-10881-5 (DOI)000299596000004 ()
##### Forskningsfinansiär
Swedish Research Council, 621-2007-6240 Tilgjengelig fra: 2011-12-21 Laget: 2011-12-21 Sist oppdatert: 2018-09-01
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On the Branch Loci of Moduli Spaces of Riemann Surfaces of Low Genera
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• 236.
On the connected branch loci of moduli spacesManuskript (preprint) (Annet vitenskapelig)

The moduli space Mg of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of such orbifold is the branch locus Bg. In this article we show that Bg is connected exactly for genera three, four, thirteen, seventeen, nineteen and fitfynine by the use automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

• 237.
On automorphisms groups of cyclic p-gonal Riemann surfaces2013Inngår i: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 57, s. 61-69Artikkel i tidsskrift (Fagfellevurdert)

In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p⩾3p⩾3 is a prime integer and the genus of the surfaces is at least (p−1)2+1(p−1)2+1. We use Fuchsian and NEC groups, and cohomology of finite groups.

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• 238.
On isolated strata of pentagonal Riemann surfaces in the branch locus of moduli spaces2012Inngår i: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 572, s. 19-24Artikkel i tidsskrift (Fagfellevurdert)
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• 239.
On isolated strata of p-gonal Riemann surfaces in the branch locus of moduli spaces2012Inngår i: Albanian Journal of Mathematics, ISSN 1930-1235, E-ISSN 1930-1235, Vol. 6, s. 11-19Artikkel i tidsskrift (Fagfellevurdert)
• 240.
On the Orbifold Structure of the Moduli Space of Riemann Surfaces of Genera Four and Five2014Inngår i: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 108, nr 2, s. 769-793Artikkel i tidsskrift (Fagfellevurdert)

The moduli space Mg, of compact Riemann surfaces of genus g has orbifold structure since Mg is the quotient space of the Tiechmüller space by the action of the mapping class group. Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space we find the orbifold structure of the moduli spaces of Riemann surfaces of genera 4 and 5.

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• 241.
On the connectedness of the branch locus of the moduli space of Riemann surfaces2010Inngår i: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 104, nr 1, s. 81-86Artikkel i tidsskrift (Fagfellevurdert)

The moduli space M-g of compact Riemann surfaces of genus g has the structure of an orbifold and the set of singular points of such orbifold is the branch locus B-g. In this article we present some results related with the topology of B-g. We study the connectedness of B-g for g andlt;= 8, the existence of isolated equisymmetric strata in the branch loci and finally we stablish the connectedness of the branch locus of the moduli space of Riemann surfaces considered as Klein surfaces. We just sketch the proof of some of the results; complete proofs will be published elsewhere.

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• 242.
Gdansk University of Technology, Poland.
A Graph – String Model of Gene Assembly in Ciliates [Grafowo-tekstowy model rekombinacji DNA u orzęsek]2006Inngår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2006, s. 521-534Konferansepaper (Fagfellevurdert)

The ciliates are a family of unicellular organisms that characterize themselves by having two types of nuclei, micro - and macronuclei. During cell mating the genetic material must change from the micronuclei to the macronuclei form. The paper summarises a formal model for this change. The model, which is described in recent works, is based on strings and graphs. It shows that inside the cell complex computational operations have to take place.

• 243.
Exact and approximate limit behaviour of the Yule trees cophenetic index2018Inngår i: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 303, s. 26-45Artikkel i tidsskrift (Fagfellevurdert)

In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on n contemporary tips. We show that this normalized phylogenetic balance index is a sub-martingale that converges almost surely and in L-2. We link our work with studies on trees without branch lengths and show that in this case the limit distribution is a contraction-type distribution, similar to the Quicksort limit distribution. In the continuous branch case we suggest approximations to the limit distribution. We propose heuristic methods of simulating from these distributions and it may be observed that these algorithms result in reasonable tails. Therefore, we propose a way based on the quantiles of the derived distributions for hypothesis testing, whether an observed phylogenetic tree is consistent with the pure-birth process. Simulating a sample by the proposed heuristics is rapid, while exact simulation (simulating the tree and then calculating the index) is a time-consuming procedure. We conduct a power study to investigate how well the cophenetic indices detect deviations from the Yule tree and apply the methodology to empirical phylogenies.

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• 244.
Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model2019Inngår i: Applicationes Mathematicae, ISSN 1233-7234, E-ISSN 1730-6280Artikkel i tidsskrift (Fagfellevurdert)

This paper builds on T. Martínez-Coronado, A. Mir, F. Rosselló and G. Valiente’s 2018 work, introducing a new balance index for trees. We show that this balance index, in the case of Aldous’s $(\beta \ge 0)$-model, converges weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.

• 245.
Department of Mathematics, Uppsala University, Uppsala, Sweden.
Phylogenetic effective sample size2016Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 407, s. 371-386Artikkel i tidsskrift (Fagfellevurdert)

In this paper I address the question—how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein-Uhlenbeck processes-the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.

• 246.
Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
Quantifying the effects of anagenetic and cladogenetic evolution2014Inngår i: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 254, s. 42-57Artikkel i tidsskrift (Fagfellevurdert)

An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both types of change, quantify the effects of speciational change via the correlation between species and attribute the proportion of change to each type. I discuss results of parameter estimation of Hominoid body size in this light. I derive mathematical formulae related to this problem, the probability generating functions of the number of speciation events along a randomly drawn lineage and from the most recent common ancestor of two randomly chosen tip species for a conditioned Yule tree. Additionally I obtain in closed form the variance of the distance from the root to the most recent common ancestor of two randomly chosen tip species.

• 247.
Simulating an infinite mean waiting time2019Inngår i: Mathematica Applicanda, ISSN 1730-2668, Vol. 47, nr 1, s. 93-102Artikkel i tidsskrift (Fagfellevurdert)

We consider a hybrid method to simulate the return time to the initial state in a critical-case birth-death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the simulation approach is to directly simulate the process, unless the simulated time exceeds some threshold and if it does, draw the return time from the tail of the power law.

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Simulating an infinite mean waiting time
• 248.
Gdansk University of Technology, Poland.
The Bootstrap and Other Methods of Testing Phylogenetic Trees2007Inngår i: Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej, 2007, s. 103-108Konferansepaper (Fagfellevurdert)

The final step of a phylogenetic analysis is the test of the generated tree. This is not a easy task for which there is an obvious methodology because we do not know the full probabilistic model of evolution. A number of methods have been proposed but there is a wide debate concerning the interpretations of the results they produce.

• 249.
Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Göteborg Sweden.
The Laplace Motion in Phylogenetic Comparative Methods2012Inngår i: Proceedings of the 18th National Conference on Applications of Mathematics in Biology and Medicine, 2012, s. 25-30Konferansepaper (Fagfellevurdert)

The majority of current phylogenetic comparative methods assume that the stochastic evolutionaryprocess is homogeneous over the phylogeny or offer relaxations of this in rather limited and usually parameter expensive ways. Here we make a preliminary investigation, bymeans of a numerical experiment, whether the Laplace motion process can offer an alternative approach.

• 250.
The phylogenetic effective sample size and jumps2018Inngår i: MATHEMATICA APPLICANDA (MATEMATYKA STOSOWANA), ISSN 1730-2668, Vol. 46, nr 1, s. 25-33Artikkel i tidsskrift (Fagfellevurdert)

The phylogenetic effective sample size is a parameter that has as its goal the quantification of the amount of independent signal in a phylogenetically correlatedsample. It was studied for Brownian motion and Ornstein-Uhlenbeck models of trait evolution. Here, we study this composite parameter when the trait is allowedto jump at speciation points of the phylogeny. Our numerical study indicates thatthere is a non-trivial limit as the effect of jumps grows. The limit depends on thevalue of the drift parameter of the Ornstein-Uhlenbeck process.

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