| 1. |
- Ameur, Adam, et al.
(författare)
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SweGen : a whole-genome data resource of genetic variability in a cross-section of the Swedish population
- 2017
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Ingår i: European Journal of Human Genetics. - : NATURE PUBLISHING GROUP. - 1018-4813 .- 1476-5438. ; 25:11, s. 1253-1260
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Tidskriftsartikel (refereegranskat)abstract
- Here we describe the SweGen data set, a comprehensive map of genetic variation in the Swedish population. These data represent a basic resource for clinical genetics laboratories as well as for sequencing-based association studies by providing information on genetic variant frequencies in a cohort that is well matched to national patient cohorts. To select samples for this study, we first examined the genetic structure of the Swedish population using high-density SNP-array data from a nation-wide cohort of over 10 000 Swedish-born individuals included in the Swedish Twin Registry. A total of 1000 individuals, reflecting a cross-section of the population and capturing the main genetic structure, were selected for whole-genome sequencing. Analysis pipelines were developed for automated alignment, variant calling and quality control of the sequencing data. This resulted in a genome-wide collection of aggregated variant frequencies in the Swedish population that we have made available to the scientific community through the website https://swefreq.nbis.se. A total of 29.2 million single-nucleotide variants and 3.8 million indels were detected in the 1000 samples, with 9.9 million of these variants not present in current databases. Each sample contributed with an average of 7199 individual-specific variants. In addition, an average of 8645 larger structural variants (SVs) were detected per individual, and we demonstrate that the population frequencies of these SVs can be used for efficient filtering analyses. Finally, our results show that the genetic diversity within Sweden is substantial compared with the diversity among continental European populations, underscoring the relevance of establishing a local reference data set.
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| 2. |
- Darpö, Erik, et al.
(författare)
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Von-Neumann Finiteness and Reversibility in some Classes of Non-Associative Algebras
- 2021
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Ingår i: Algebras and Representation Theory. - : Springer Science and Business Media LLC. - 1386-923X .- 1572-9079. ; 24, s. 1245-1258
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Tidskriftsartikel (refereegranskat)abstract
- We investigate criteria for von-Neumann finiteness and reversibility in some classes of non-associative algebras. Types of algebras that are studied include alternative, flexible, quadratic and involutive algebras, as well as algebras obtained by the Cayley–Dickson doubling process. Our results include precise criteria for von-Neumann finiteness and reversibility of involutive algebras in terms of isomorphism types of their 3-dimensional subalgebras. © 2020, The Author(s).
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| 3. |
- Halvorsen, Matthew, et al.
(författare)
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Increased burden of ultra-rare structural variants localizing to boundaries of topologically associated domains in schizophrenia
- 2020
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Ingår i: Nature Communications. - : Springer Science and Business Media LLC. - 2041-1723 .- 2041-1723. ; 11:1, s. 1842-
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Tidskriftsartikel (refereegranskat)abstract
- Despite considerable progress in schizophrenia genetics, most findings have been for large rare structural variants and common variants in well-imputed regions with few genes implicated from exome sequencing. Whole genome sequencing (WGS) can potentially provide a more complete enumeration of etiological genetic variation apart from the exome and regions of high linkage disequilibrium. We analyze high-coverage WGS data from 1162 Swedish schizophrenia cases and 936 ancestry-matched population controls. Our main objective is to evaluate the contribution to schizophrenia etiology from a variety of genetic variants accessible to WGS but not by previous technologies. Our results suggest that ultra-rare structural variants that affect the boundaries of topologically associated domains (TADs) increase risk for schizophrenia. Alterations in TAD boundaries may lead to dysregulation of gene expression. Future mechanistic studies will be needed to determine the precise functional effects of these variants on biology.
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| 4. |
- Lännström, Daniel, 1989-
(författare)
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The structure of epsilon-strongly graded rings with applications to Leavitt path algebras and Cuntz-Pimsner rings
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The research field of graded ring theory is a rich area of mathematics with many connections to e.g. the field of operator algebras. In the last 15 years, algebraists and operator algebraists have defined algebraic analogues of important operator algebras. Some of those analogues are rings that come equipped with a group grading. We want to reach a better understanding of the graded structure of those analogue rings. Among group graded rings, the strongly graded rings stand out as being especially well-behaved. The development of the general theory of strongly graded rings was initiated by Dade in the 1980s and since then numerous structural results have been established for strongly graded rings. In this thesis, we study the class of epsilon-strongly graded rings which was recently introduced by Nystedt, Öinert and Pinedo. This class is a natural generalization of the well-studied class of unital strongly graded rings. Our aim is to lay the foundation for a general theory of epsilon-strongly graded rings generalizing the theory of strongly graded rings. This thesis is based on three articles. The first two articles mainly concern structural properties of epsilon-strongly graded rings. In the first article, we investigate a functorial construction called the induced quotient group grading. In the second article, using results from the first article, we generalize the Hilbert Basis Theorem for strongly graded rings to epsilon-strongly graded rings and apply it to Leavitt path algebras. In the third article, we study the graded structure of algebraic Cuntz-Pimsner rings. In particular, we obtain a partial classification of unital strongly, epsilon-strongly and nearly epsilon-strongly graded Cuntz-Pimsner rings up to graded isomorphism.
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| 5. |
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| 6. |
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| 7. |
- Nystedt, Patrik, 1971-
(författare)
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A proof of the law of sines using the law of cosines
- 2017
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Ingår i: Mathematics Magazine. - : Informa UK Limited. - 0025-570X .- 1930-0980. ; 90:3, s. 180-181
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Tidskriftsartikel (refereegranskat)abstract
- We give a proof of the law of sines using the law of cosines. © Mathematical Association of America.
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| 8. |
- Nystedt, Patrik, 1971-
(författare)
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Arc length of function graphs via Taylor’s formula
- 2021
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Ingår i: International Journal of Mathematical Education in Science and Technology. - 0020-739X .- 1464-5211. ; 52:2, s. 310-323
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Tidskriftsartikel (refereegranskat)abstract
- We use Taylor’s formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of functions f with the property that (Formula presented.) has a primitive, including classical examples by Neile, van Heuraet and Fermat, as well as more recent ones induced by Pythagorean triples of functions. We also discuss potential benefits for our proposed definition of arc length in introductory calculus courses. © 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
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| 9. |
- Nystedt, Patrik, 1971-, et al.
(författare)
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Artinian and noetherian partial skew groupoid rings
- 2018
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Ingår i: Journal of Algebra. - : Academic Press. - 0021-8693 .- 1090-266X. ; 503, s. 433-452
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Tidskriftsartikel (refereegranskat)abstract
- Let α={α_g : R_{g^{−1}}→R_g}_{g∈mor(G)} be a partial action of a groupoid G on a (not necessarily associative) ring R and let S=R⋆G be the associated partial skew groupoid ring. We show that if α is global and unital, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). We use this result to prove that if α is unital and R is alternative, then S is left (right) artinian if and only if R is left (right) artinian and R_g={0}, for all but finitely many g∈mor(G). This result applies to partial skew group rings, in particular. Both of the above results generalize a theorem by J. K. Park for classical skew group rings, i.e. the case when R is unital and associative, and G is a group which acts globally on R. We provide two additional applications of our main results. Firstly, we generalize I. G. Connell's classical result for group rings by giving a characterization of artinian (not necessarily associative) groupoid rings. This result is in turn applied to partial group algebras. Secondly, we give a characterization of artinian Leavitt path algebras. At the end of the article, we relate noetherian and artinian properties of partial skew groupoid rings to those of global skew groupoid rings, as well as establish two Maschke-type results, thereby generalizing results by M. Ferrero and J. Lazzarin for partial skew group rings to the case of partial skew groupoid rings.
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| 10. |
- Nystedt, Patrik, 1971-, et al.
(författare)
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Epsilon-strongly graded rings, separability and semisimplicity
- 2018
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 514, s. 1-24
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the class of epsilon-strongly graded rings and show that it properly contains both the class of strongly graded rings and the class of unital partial crossed products. We determine precisely when an epsilon-strongly graded ring is separable over its principal component. Thereby, we simultaneously generalize a result for strongly group graded rings by NÇŽstÇŽsescu, Van den Bergh and Van Oystaeyen, and a result for unital partial crossed products by Bagio, Lazzarin and Paques. We also show that the class of unital partial crossed products appears in the class of epsilon-strongly graded rings in a fashion similar to how the classical crossed products present themselves in the class of strongly graded rings. Thereby, we obtain, in the special case of unital partial crossed products, a short proof of a general result by Dokuchaev, Exel and Simón concerning when graded rings can be presented as partial crossed products. We also provide some interesting classes of examples of separable epsilon-strongly graded rings, with finite as well as infinite grading groups. In particular, we obtain an answer to a question raised by Le Bruyn, Van den Bergh and Van Oystaeyen in 1988. © 2018 Elsevier Inc.
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