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• 301.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
An equivalence to the Gleason problem2010In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 370, no 2, p. 373-378Article in journal (Refereed)

In this article we study the Gleason problem locally. A new method for solving the Gleason A problem is presented. This is done by showing an equivalent statement to the Gleason A problem. In order to prove this statement, necessary and a sufficient conditions for a bounded domain to have the Gleason A property are found. Also an example of a bounded but not smoothly-bounded domain in C(n) is given, which satisfies the sufficient condition at the origin, and hence has the Gleason A property there.

• 302.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Analytic properties in the spectrum of certain Banach algebras2009In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 261, no 1, p. 189-200Article in journal (Refereed)
• 303.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Ideals and boundaries in Algebras of Holomorphic functions2006Doctoral thesis, monograph (Other academic)

We investigate the spectrum of certain Banach algebras. Properties like generators of maximal ideals and generalized Shilov boundaries are studied. In particular we show that if the ∂-equation has solutions in the algebra of bounded functions or continuous functions up to the boundary of a domain D ⊂⊂ Cn then every maximal ideal over D is generated by the coordinate functions. This implies that the fibres over D in the spectrum are trivial and that the projection on Cn of the n − 1 order generalized Shilov boundary is contained in the boundary of D.

For a domain D ⊂⊂ Cn where the boundary of the Nebenhülle coincide with the smooth strictly pseudoconvex boundary points of D we show that there always exist points p ∈ D such that D has the Gleason property at p.

If the boundary of an open set U is smooth we show that there exist points in U such that the maximal ideals over those points are generated by the coordinate functions.

An example is given of a Riemann domain, Ω, spread over Cn where the fibers over a point p ∈ Ω consist of m > n elements but the maximal ideal over p is generated by n functions.

• 304.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Nebenhulle and the Gleason problem2010In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 1, p. 267-273Article in journal (Refereed)

This article concerns the Gleason property as a local phenomenon. We prove that there always exists an open set where the domain D (sic) C(2) has the Gleason beta property whenever the boundary of the Nebenhulle of D coincides with a C(2) smooth part of the boundary bD; here beta is either one of the Banach algebras, H(infinity) or A. As an easy consequence of this, we see that if the extremal boundary points are C(2)-smooth, then D has the Gleason beta property close to those points. Also a partial derivative-problem for locally supported forms is solved.

• 305.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Nebenhülle and the Gleason problem2010In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 1, p. 267-273Article in journal (Refereed)
• 306.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Spectrum of certain Banach algebras and $\overline\partial$-problems2007In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 90, no 1, p. 51-58Article in journal (Refereed)
• 307.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Trivial generators for nontrivial fibres2008In: MATHEMATICA BOHEMICA, ISSN 0862-7959, Vol. 133, no 2, p. 121-131Article in journal (Refereed)

Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in $\mathbb{C}^n$ where the fibre is nontrivial, has to exceed $n$. This is shown not to be the case.

• 308.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Spectrum of certain Banach algebras and ∂-problems2007In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 90, no 1, p. 51-58Article in journal (Refereed)
• 309.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
A note on B-envelope of holomorphy and B-extendable domains2008In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 53, no 4, p. 307-309Article in journal (Refereed)

Let   be a Banach Algebra on a Riemann domain X over  . We show that under certain conditions on   and X, all functions in   can be extended to functions in  where   is the  -envelope of holomorphy.

• 310.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
En tidsseriestudie av varviga sjösediment från Kassjön2001Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis aims to analyse a time series containing the annual accumulation rate of minerogenic matter in the lake Kassjön. First there is a theoretical survey of some frequently used tools for the analysis of time series in the time domain and in the frequency domain. This survey is followed by a simulation study that illustrates how the theoretical tools work in practice. After this, the time series "toolbox" is used to analyse the time series from Kassjön (5701 data points). The time series data is analysed in the time domain as well as in the frequency domain. The time domain study focuses on the behaviour of the autocorrelation and the partial autocorrelation function. The frequency domain study analyses the standard periodogram and the periodogram smoothed with Tukey weights. The periodogram study tells us that the important components - for the behaviour of the series - are those with low angular frequency which corresponds to slow oscillations. The interesting cycles are approximately 330 years and can be identified more or less throughout the series.

• 311.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
A note on path factors of (3,4)-biregular bipartite graphsManuscript (preprint) (Other academic)
• 312.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
A note on path factors of (3,4)-biregular bipartite graphs2011In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 18, no 1, p. P218-Article in journal (Refereed)

A proper edge coloring of a graph G with colors 1,2,3, ... is called an interval coloring if the colors on the edges incident with any vertex are consecutive. A bipartite graphis (3,4)-biregular if all vertices in one part have degree 3 and all vertices in the other part have degree 4. Recently it was proved [J. Graph Theory 61 (2009), 88-97] that if such a graph G has a spanning subgraph whose components are paths with end points at 3-valent vertices and lengths in {2,4,6,8}, then G has an interval coloring. It was also conjectured that every simple (3,4)-biregular bipartite graph has such a subgraph. We provide some evidence for this conjecture by proving that a simple (3,4)-biregular bipartite graph has a spanning subgraph whose components are nontrivial paths with endpoints at 3-valent vertices and lengths not exceeding 22.

• 313.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Coloring graphs from random lists of fixed sizeManuscript (preprint) (Other academic)
• 314.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Coloring graphs from random lists of size 2Manuscript (preprint) (Other academic)
• 315.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Coloring graphs from random lists of size 22012In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 33, no 2, p. 168-181Article in journal (Refereed)

Let G = G(n) be a graph on n vertices with girth at least g and maximum degree bounded by some absolute constant Delta. Assign to each vertex v of G a list L(v) of colors by choosing each list independently and uniformly at random from all 2-subsets of a color set e of size sigma (n). In this paper we determine, for each fixed g and growing n, the asymptotic probability of the existence of a proper coloring phi such that phi(v) is an element of L(v) for all v is an element of V(G). In particular, we show that if g is odd and sigma (n) = omega(n(1/(2g-2))), then the probability that G has a proper coloring from such a random list assignment tends to 1 as n --> infinity. Furthermore, we show that this is best possible in the sense that for each fixed odd g and each n >= g, there is a graph H = H(n, g) with bounded maximum degree and girth g, such that if sigma (n) = 0(n(1/(2g-2))), then the probability that H has a proper coloring from such a random list assignment tends to 0 as n --> infinity. A corresponding result for graphs with bounded maximum degree and even girth is also given. Finally, by contrast, we show that for a complete graph on n vertices, the property of being colorable from random lists of size 2, where the lists are chosen uniformly at random from a color set of size sigma (n), exhibits a sharp threshold at sigma (n) = 2n. (C) 2011 Elsevier Ltd. All rights reserved.

• 316.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
On avoiding some families of arrays2012In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 312, no 5, p. 963-972Article in journal (Refereed)

An n×n array A with entries from {1,…,n} is avoidable if there is an n×n Latin square L such that no cell in L contains a symbol that occurs in the corresponding cell in A. We show that the problem of determining whether an array that contains at most two entries per cell is avoidable is NP-complete, even in the case when the array has entries from only two distinct symbols. Assuming that PNP, this disproves a conjecture by Öhman. Furthermore, we present several new families of avoidable arrays. In particular, every single entry array (arrays where each cell contains at most one symbol) of order n≥2k with entries from at most k distinct symbols and where each symbol occurs in at most n−2 cells is avoidable, and every single entry array of order n, where each of the symbols 1,…,n occurs in at most cells, is avoidable. Additionally, if k≥2, then every single entry array of order at least n≥4, where at most k rows contain non-empty cells and where each symbol occurs in at most nk+1 cells, is avoidable.

• 317.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
On some graph coloring problems2011Doctoral thesis, comprehensive summary (Other academic)
• 318.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Vertex coloring complete multipartite graphs from random lists of size 22011In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 311, no 13, p. 1150-1157Article in journal (Refereed)

Let Ks×m be the complete multipartite graph with s parts and m vertices in each part. Assign to each vertex v of Ks×m a list L(v) of colors, by choosing each list uniformly at random from all 2-subsets of a color set C of size σ(m). In this paper we determine, for all fixed s and growing m, the asymptotic probability of the existence of a proper coloring φ, such that φ(v)∈L(v) for all vV(Ks×m). We show that this property exhibits a sharp threshold at σ(m)=2(s−1)m.

• 319. Casselgren, Carl Johan
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Coloring Complete and Complete Bipartite Graphs from Random Lists2016In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 32, no 2, p. 533-542Article in journal (Refereed)

Assign to each vertex v of the complete graph on n vertices a list L(v) of colors by choosing each list independently and uniformly at random from all f(n)-subsets of a color set , where f(n) is some integer-valued function of n. Such a list assignment L is called a random (f(n), [n])-list assignment. In this paper, we determine the asymptotic probability (as ) of the existence of a proper coloring of , such that for every vertex v of . We show that this property exhibits a sharp threshold at . Additionally, we consider the corresponding problem for the line graph of a complete bipartite graph with parts of size m and n, respectively. We show that if , , and L is a random (f(n), [n])-list assignment for the line graph of , then with probability tending to 1, as , there is a proper coloring of the line graph of with colors from the lists.

• 320. Casselgren, Carl Johan
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Completing partial Latin squares with one filled row, column and symbol2013In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 313, no 9, p. 1011-1017Article in journal (Refereed)

Let P be an n x n partial Latin square every non-empty cell of which lies in a fixed row r, a fixed column c or contains a fixed symbols. Assume further that s is the symbol of cell (r, c) in P. We prove that P is completable to a Latin square if n >= 8 and n is divisible by 4, or n <= 7 and n is not an element of {3, 4, 5}. Moreover, we present a polynomial algorithm for the completion of such a partial Latin square. (C) 2013 Elsevier B.V. All rights reserved.

• 321. Casselgren, Carl Johan
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Edge precoloring extension of hypercubesManuscript (preprint) (Other academic)

We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most (d-1) edges of the d-dimensional hypercube Qd can be extended to a proper d-edge coloring of Qd. Additionally, we characterize which partial edge colorings of Qd with precisely d precolored edges are extendable to proper d-edge colorings of Qd.

• 322. Casselgren, Carl Johan
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Latin cubes with forbidden entries2019In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 26, no 1, article id P1.2Article in journal (Refereed)

We consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant y>0 such that if n=2k and A is a 3-dimensional n×n×n array where every cell contains at most γn symbols, and every symbol occurs at most γn times in every line of A, then A is avoidable; that is, there is a Latin cube L of order n such that for every 1 ≤ i,j,k ≤ n, the symbol in position (i,j,k) of L does not appear in the corresponding cell of A.

• 323. Casselgren, Carl Johan
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Restricted extension of sparse partial edge colorings of hypercubesManuscript (preprint) (Other academic)

We consider the following type of question: Given a partial proper d-edge coloring of the d-dimensional hypercube Qd, and lists of allowed colors for the non-colored edges of Qd, can we extend the partial coloring to a proper d-edge coloring using only colors from the lists? We prove that this question has a positive answer in the case when both the partial coloring and the color lists satisfy certain sparsity conditions.

• 324. Casselgren, Carl Johan
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Latin cubes of even order with forbidden entriesManuscript (preprint) (Other academic)

We consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant γ>0 such that if n=2t and A is a 3-dimensional n×n×n array where every cell contains at most γn symbols, and every symbol occurs at most γn times in every line of A, then A is avoidable; that is, there is a Latin cube L of order n such that for every 1≤i,j,k≤n, the symbol in position (i,j,k) of L does not appear in the corresponding cell of A.

• 325. Cavenagh, Nicholas J.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Partial latin squares are avoidable2006Report (Other academic)
• 326.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Modelling Credit Risk: Estimation of Asset and Default Correlation for an SME Portfolio2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

When banks lend capital to counterparties they take on a risk, known as credit risk which traditionally has been the largest risk exposure for banks. To be protected against potential default losses when lending capital, banks must hold a regulatory capital that is based on a regulatory formula for calculating risk weighted assets (RWA). This formula is part of the Basel Accords and it is implemented in the legal system of all European Union member states. The key parameters of the RWA formula are probability of default, loss given default and asset correlation. Banks today have the option to estimate the probability of default and loss given default by internal models however the asset correlation must be determined by a formula provided by the legal framework.

This project is a ﬁrst approach for Handelsbanken to study what would happen if banks were allowed to estimate asset correlation by internal models. We assess two models for estimating the asset correlation of a portfolio of Small and Medium Enterprices (SME). The estimates are compared with the asset correlation given by the regulatory formula and with estimates for another parameter called default correlation. The models are validated using predicted historical data and Monte-Carlo Simulations. For the studied SME portfolio, the models give similar estimates for the asset correlations and the estimates are lower than those given by the regulatory formula. This would imply a lower capital requirement if banks were allowed to use internal models to estimate the asset correlation used in the RWA formula. Default correlation, if not used synonymously with asset correlation, is shown to be another measure and should not be used in the RWA formula.

• 327.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
A general Dirichlet problem for the complex Monge-Ampère operator2008In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 94, no 2, p. 131-147Article in journal (Refereed)
• 328.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Convergence in Capacity2012In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 55, no 2, p. 242-248Article in journal (Refereed)

In this note we study the convergence of sequences of Monge-Ampere measures {(dd(c)u(s))(n)}, where {u(s)} is a given sequence of plurisubharmonic functions, converging in capacity.

• 329.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Explicit calculation of a Monge-Ampère measure2000Conference proceedings (editor) (Other academic)
• 330.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Maximal plurisubharmonic functions2009In: Uzbek Mathematical Journal, no 1, p. 10-16Article in journal (Other academic)
• 331.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Measures of finite pluricomplex energy2019In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, no 1, p. 203-213Article in journal (Refereed)

We study a complex Monge-Ampere type equation of the form (dd(c)u)(n) = ke(-u)dV/integral e(-u)dV.

• 332.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Potentials with respect to the pluricomplex Green function2012In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, p. 107-111Article in journal (Refereed)

For μ a positive measure, we estimate the pluricomplex potential of μ, Pμ(x)=∫Ωg(x,y)dμ(y), where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.

• 333.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
The General Definition of the Complex Monge-Ampère Operator2004In: Annales de l'Institut Fourier, ISSN 0373-0956, Vol. 54, no 1, p. 159-179Article in journal (Refereed)
• 334.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
The gradient lemma2007In: Annales Polonici Mathematici, ISSN 0066-2216, Vol. 91, no 2-3, p. 143-146Article in journal (Refereed)
• 335.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Weak*-convergence of Monge-Ampère measures2006In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 254, no 3, p. 505-508Article in journal (Refereed)
• 336.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Subextension and approximation of negative plurisubharmonic functions2008In: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 56, p. 593-601Article in journal (Refereed)
• 337.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Monge-Ampère boundary measures2009In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, no 2, p. 175-196Article in journal (Refereed)

We study swept-out Monge–Ampère measures of plurisubharmonic functions and boundary values related to those measures.

• 338.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
The equation of complex Monge-Ampère type and stability of solutions2006In: Mathematische Annalen, ISSN 0025-5831, Vol. 334, no 4, p. 713-729Article in journal (Refereed)
• 339.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Subextension of plurisubharmonic functions with weak singularities2005In: Mathematische Zeitschrift, ISSN 0025-5874, Vol. 250, no 1, p. 7-22Article in journal (Refereed)
• 340.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
A Monge-Ampère norm for delta-plurisubharmonic functions2005In: Mathematica Scandinavica, ISSN 0025-5521, Vol. 97, no 2, p. 201-216Article in journal (Refereed)
• 341.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2-6-20-3 Shiro-machi, Hikone, Shiga 522-0068, Japan.
Representation of magnetic fields by jump theorem for harmonic forms2008In: Mathematical Proceedings of the Royal Irish Academy, ISSN 1393-7197, E-ISSN 2009-0021, Vol. 108A, no 1, p. 7-17Article in journal (Refereed)

It has previously been shown that a surface current density J on a closed Σ of class C°° in R3 induces a static magnetic field Bj in R3 \ Σ, which has some discontinuity along Σ. In this note, we represent Bj by use of jump theorem for harmonic forms in the case where Σ is of class Οω. We then apply this result to prove the existence of a surface current density J, which induces the nonzero magnetic field Bj such that Bj = 0 inside (or outside) of the domain bounded by Σ in R3. This has previously been called the equilibrium magnetic field for Σ.

• 342.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Construction of equilibrium magnetic vector potentials2001In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 15, no 4, p. 301-331Article in journal (Refereed)
• 343.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Subextension of plurisubharmonic functions with bounded Monge-Ampère mass2003In: Comptes rendus de l'Académie des sciences. Série 1, Mathématique, ISSN 0764-4442, E-ISSN 1778-3577, Vol. 336, no 4, p. 305-308Article in journal (Refereed)
• 344. Cenanovic, Mirza
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Cut finite element modeling of linear membranes2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 310, p. 98-111Article in journal (Refereed)

We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus, i.e., with the equilibrium equations pointwise projected onto the tangent plane of the surface to create a pointwise planar problem in the tangential direction. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization of the membrane comes from a Galerkin method using the restriction of 3D basis functions (linear or trilinear) to the surface representing the membrane. In the case of coupling to 3D elasticity, we view the membrane as giving additional stiffness contributions to the standard stiffness matrix resulting from the discretization of the three-dimensional continuum.

• 345. Cenanovic, Mirza
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Minimal surface computation using a finite element method on an embedded surface2015In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 104, no 7, p. 502-512Article in journal (Refereed)

We suggest a finite element method for finding minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a distance function using linear tetrahedral finite elements, and the finite element discretization is carried out on the piecewise planar isosurface using the shape functions from the background three-dimensional mesh used to represent the distance function. A recently suggested stabilized scheme for finite element approximation of the mean curvature vector is a crucial component of the method.

• 346.
Umeå University, Faculty of Science and Technology, Department of Molecular Biology (Faculty of Science and Technology).
Umeå University, Faculty of Science and Technology, Department of Molecular Biology (Faculty of Science and Technology). Umeå University, Faculty of Science and Technology, Department of Chemistry. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Department of Molecular Biology (Faculty of Science and Technology).
Elongator Complex Influences Telomeric Gene Silencing and DNA Damage Response by Its Role in Wobble Uridine tRNA Modification2011In: PLoS genetics, ISSN 1553-7404, Vol. 7, no 9, p. e1002258-Article in journal (Refereed)

Elongator complex is required for formation of the side chains at position 5 of modified nucleosides 5-carbamoylmethyluridine (ncm(5)U(34)), 5-methoxycarbonylmethyluridine (mcm(5)U(34)), and 5-methoxycarbonylmethyl-2-thiouridine (mcm(5)s(2)U(34)) at wobble position in tRNA. These modified nucleosides are important for efficient decoding during translation. In a recent publication, Elongator complex was implicated to participate in telomeric gene silencing and DNA damage response by interacting with proliferating cell nuclear antigen (PCNA). Here we show that elevated levels of tRNA(Lys) (s(2) ) (UUU), tRNA(Gln) (s(2) ) (UUG), and tRNA(Glu) (s(2) ) (UUC), which in a wild-type background contain the mcm(5)s(2)U nucleoside at position 34, suppress the defects in telomeric gene silencing and DNA damage response observed in the Elongator mutants. We also found that the reported differences in telomeric gene silencing and DNA damage response of various elp3 alleles correlated with the levels of modified nucleosides at U(34). Defects in telomeric gene silencing and DNA damage response are also observed in strains with the tuc2Δ mutation, which abolish the formation of the 2-thio group of the mcm(5)s(2)U nucleoside in tRNA(Lys) (mcm(5) (s(2) ) (UUU) ), tRNA(Gln) (mcm(5) (s(2) ) (UUG) ), and tRNA(Glu) (mcm(5) (s(2) ) (UUC) ). These observations show that Elongator complex does not directly participate in telomeric gene silencing and DNA damage response, but rather that modified nucleosides at U(34) are important for efficient expression of gene products involved in these processes. Consistent with this notion, we found that expression of Sir4, a silent information regulator required for assembly of silent chromatin at telomeres, was decreased in the elp3Δ mutants.

• 347. Chen, Chuchu
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Conservative methods for stochastic differential equations with a conserved quantity2016In: International Journal of Numerical Analysis and Modeling, ISSN 1923-2942, Vol. 13, no 3, p. 435-456Article in journal (Refereed)

This paper proposes a novel conservative method for the numerical approximation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is 1 if noises are commutative and that the weak order is 1 in the general case. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results.

• 348. Chen, Xiaojie
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.
Parent-preferred dispersal promotes cooperation in structured populations2019In: Proceedings of the Royal Society of London. Biological Sciences, ISSN 0962-8452, E-ISSN 1471-2954, Vol. 286, no 1895, article id 20181949Article in journal (Refereed)

Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth-death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.

• 349. Chen, Xiaojie
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
First carrot, then stick: how the adaptive hybridization of incentives promotes cooperation2015In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 12, no 102, article id 20140935Article in journal (Refereed)

Social institutions often use rewards and penalties to promote cooperation. Providing incentives tends to be costly, so it is important to find effective and efficient policies for the combined use of rewards and penalties. Most studies of cooperation, however, have addressed rewarding and punishing in isolation and have focused on peer-to-peer sanctioning as opposed to institutional sanctioning. Here, we demonstrate that an institutional sanctioning policy we call 'first carrot, then stick' is unexpectedly successful in promoting cooperation. The policy switches the incentive from rewarding to punishing when the frequency of cooperators exceeds a threshold. We find that this policy establishes and recovers full cooperation at lower cost and under a wider range of conditions than either rewards or penalties alone, in both well-mixed and spatial populations. In particular, the spatial dynamics of cooperation make it evident how punishment acts as a 'booster stage' that capitalizes on and amplifies the pro-social effects of rewarding. Together, our results show that the adaptive hybridization of incentives offers the 'best of both worlds' by combining the effectiveness of rewarding in establishing cooperation with the effectiveness of punishing in recovering it, thereby providing a surprisingly inexpensive and widely applicable method of promoting cooperation.

• 350. Chen, Zhi-Qiang
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Method for accurate fiber length determination from increment cores for large-scale population analyses in Norway spruce2016In: Holzforschung, ISSN 0018-3830, E-ISSN 1437-434X, Vol. 70, no 9, p. 829-838Article in journal (Refereed)

Fiber (tracheid) length is an important trait targeted for genetic and silvicultural improvement. Such studies require large-scale non-destructive sampling, and accurate length determination. The standard procedure for non-destructive sampling is to collect increment cores, singularize their cells by maceration, measure them with optical analyzer and apply various corrections to suppress influence of non-fiber particles and cut fibers, as fibers are cut by the corer. The recently developed expectation-maximization method (EM) not only addresses the problem of non-fibers and cut fibers, but also corrects for the sampling bias. Here, the performance of the EM method has been evaluated by comparing it with length-weighing and squared length-weighing, both implemented in fiber analyzers, and with microscopy data for intact fibers, corrected for sampling bias, as the reference. This was done for 12-mm increment cores from 16 Norway spruce (Picea abies (L.) Karst) trees on fibers from rings 8-11 (counted from pith), representing juvenile wood of interest in breeding programs. The EM-estimates provided mean-fiber-lengths with bias of only +2.7% and low scatter. Length-weighing and length2-weighing gave biases of -7.3% and +9.3%, respectively, and larger scatter. The suggested EM approach constitutes a more accurate non-destructive method for fiber length (FL) determination, expected to be applicable also to other conifers.

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