| 1. |
- Eriksson, Kimmo, et al.
(författare)
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Bentley’s conjecture on popularity toplist turnover under random copying
- 2010
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Ingår i: The Ramanujan journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 23, s. 371-396
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Tidskriftsartikel (refereegranskat)abstract
- Bentley et al studied the turnover rate in popularity toplists in a ’random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ√μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.
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| 2. |
- Geli, Patricia
(författare)
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Modeling the Mechanism of Postantibiotic Effect and Determining Implications for Dosing Regimens
- 2009
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Ingår i: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 59:5, s. 1416-1432
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Tidskriftsartikel (refereegranskat)abstract
- A stochastic model is proposed to explain one possible underlying mechanism of the postantibiotic effect (PAE). This phenomenon, of continued inhibition of bacterial growth after removal of the antibiotic drug, is of high relevance in the context of optimizing dosing regimens. One clinical implication of long PAE lies in the possibility of increasing intervals between drug administrations. The model describes the dynamics of synthesis, saturation and removal of penicillin binding proteins (PBPs). High fractions of saturated PBPs are in the model associated with a lower growth capacity of bacteria. An analytical solution for the bivariate probability of saturated and unsaturated PBPs is used as a basis to explore optimal antibiotic dosing regimens. Our finding that longer PAEs do not necessarily promote for increased intervals between doses, might help for our understanding of data provided from earlier PAE studies and for the determination of the clinical relevance of PAE in future studies.
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| 3. |
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| 4. |
- Bergkvist, Tanja, 1974-
(författare)
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Asymptotics of Eigenpolynomials of Exactly-Solvable Operators
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The main topic of this doctoral thesis is asymptotic properties of zeros in polynomial families arising as eigenfunctions to exactly-solvable differential operators. The study was initially inspired by a number of striking results from computer experiments performed by G. Masson and B. Shapiro for a more restrictive class of operators. Our research is also motivated by a classical question going back to S. Bochner on a general classification of differential operators possessing an infinite sequence of orthogonal eigenpolynomials. In general however, the sequence of eigenpolynomials of an exactly-solvable operator is not an orthogonal system and it can therefore not be studied by means of the extensive theory known for such systems. Our study can thus be considered as the first steps to a natural generalization of the asymptotic behaviour of the roots of classical orthogonal polynomials. Exactly-solvable operators split into two major classes: non-degenerate and degenerate. We prove that in the former case, as the degree tends to infinity, the zeros of the eigenpolynomial are distributed according to a certain probability measure which is compactly supported on a tree and which depends only on the leading term of the operator. Computer experiments indicate the existence of a limiting root measure in the degenerate case too, but that it is compactly supported (conjecturally on a tree) only after an appropriate scaling which is conjectured (and partially proved) in this thesis. One of the main technical tools in this thesis is the Cauchy transform of a probability measure, which in the considered situation satisfies an algebraic equation. Due to the connection between the asymptotic root measure and its Cauchy transform it is therefore possible to obtain detailed information on the limiting zero distribution.
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| 5. |
- Berglund, Alexander, 1981-
(författare)
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Minimal models in algebra, combinatorics and topology
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The thesis consists of seven papers.In Paper I, II, III, IV and V, we study homological invariants of monomial rings — rings of the form R = k[x1, . . . , xn]/I where I is a monomial ideal in the polynomial ring k[x1, . . . , xn] over a field k — and we study combinatorial aspects of these invariants. Specifically, we study the Poincaré series PR(z), the homotopy Lie algebra of the Koszul complex π*(KR), and the following question: When is R a Golod ring? We find a formula for the Poincaré series in terms of homology groups of lower intervals in a finite lattice KI , and we relate the Golod property of R with the Cohen-Macaulay property of KI . A description of the homotopy Lie algebra π*(KR) in terms of the cohomology of a certain combinatorially defined ∞-algebra is given, and it is used to prove that R is Golod if and only if the homology algebra H*(KR) has trivial multiplication. We prove that a certain combinatorial criterion, called the strong gcd-condition, implies Golodness of R and we relate this criterion to (non-pure) shellability of simplicial complexes.In Paper VI, we lay the foundations of a cohomology theory for associative algebras, called Cofinite Hochschild cohomology, which may be seen as a continuous version of Hochschild cohomology. We prove that under reasonable hypotheses, the natural map from cofinite cohomology to Hochschild cohomology is an isomorphism for commutative noetherian algebras.In Paper VII, we extend homological perturbation theory of chain complexes to encompass (co)algebra structures over (co)operads. This is done by ‘thickening’ the category of (co)algebras over a (co)operad, and the functorial properties of the thick categories are carefully worked out. As an application, this theory provides means of proving transfer theorems for algebras over a large class of operads.
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| 6. |
- Britton, Tom, et al.
(författare)
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The early stage behaviour of a stochastic SIR epidemic with term-time forcing
- 2009
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 46:4, s. 975-992
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Tidskriftsartikel (refereegranskat)abstract
- The general stochastic SIR epidemic in a closed population under the influence of a term-time forced environment is considered. An 'environment' in this context is any external factor that influences the contact rate between individuals in the population, but is itself unaffected by the population. Here 'term-time forcing' refers to discontinuous but cyclic changes in the contact rate. The inclusion of such an environment into the model is done by replacing a single contact rate λ with a cyclically alternating renewal process with k different states denoted {A(t)}t≥0. Threshold conditions in terms of R⋆ are obtained, such that R⋆ > 1 implies that π, the probability of a large outbreak, is strictly positive. Examples are given where π is evaluated numerically from which the impact of the distribution of the time periods that Λ(t) spends in its different states is clearly seen.
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| 7. |
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| 8. |
- Emtander, Eric, 1979-
(författare)
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Betti numbers of hypergraphs
- 2009
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Ingår i: Communications in Algebra. - : Informa UK Limited. - 0092-7872 .- 1532-4125. ; 37:5, s. 1545-1571
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we study some algebraic properties of hypergraphs, in particular their Betti numbers. We define some different types of complete hypergraphs, which to the best of our knowledge are not previously considered in the literature. Also, in a natural way, we define a product on hypergraphs, which in a sense is dual to the join operation on simplicial complexes. For such product, we give a general formula for the Betti numbers, which specializes neatly in case of linear resolutions.
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| 9. |
- Emtander, Eric, 1979-
(författare)
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Betti numbers of some semigroup rings
- 2010
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Ingår i: Journal of Commutative Algebra. - 1939-2346. ; 2:3, s. 387-400
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Tidskriftsartikel (refereegranskat)
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| 10. |
- Emtander, Eric, 1979-, et al.
(författare)
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Componentwise linearity of ideals arising from graphs
- 2008
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Ingår i: Le Matematiche. - Catania : Dipartimento di Matematica e Informatica, University of Catania. - 2037-5298 .- 0373-3505. ; 63:2, s. 185-189
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Tidskriftsartikel (refereegranskat)
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