| 1. |
- Adrian Meredith, Jenny, 1971-, et al.
(författare)
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Design and Synthesis of BACE-1 Inhibitors Containing a New Hydroxyethylene (HE) Scaffold: Potent activities in a cellular assay
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In a preceding report from our group we disclosed the development of a novel HE transition state isostere with a difluorophenoxymethyl side chain in the P1 position and a methoxy group in the P1’ position furnishing highly potent inhibitors of BACE-1 (i.e. lead compound 1), which moreover exhibit very promising selectivity over cathepsin D. In a continuation of this work with the aim at improving on the cell-based activity and pharmacokinetic properties, we have further developed the SAR for the P1 side chain of inhibitor 1 whereby the P1 side chain oxygen has been substituted for an amine, a carbon or a bond. The chemistry developed for the previous HE inhibitor structure 1 has now been extended to readily accommodate the introduction of new P1 side chains into this new HE scaffold. These modifications have given rise to several highly potent inhibitors where the most potent displayed a BACE-1 Ki value of 0.2 nM and a cell-based Aβ40 IC50 value of 9 nM. Thus, regarding the enzyme inhibition in the cell assay a more than 600-fold improvement compared to compound 1 was achieved via minor structural alterations.
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| 2. |
- Björklund, Michael, 1981, et al.
(författare)
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ANALYTIC PROPERTIES OF APPROXIMATE LATTICES
- 2020
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Ingår i: Annales de lInstitut Fourier. - 0373-0956. ; 70:5, s. 1903-1950
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a notion of cocycle-induction for strong uniform approximate lattices in locally compact second countable groups and use it to relate (relative) Kazhdan- and Haagerup-type of approximate lattices to the corresponding properties of the ambient locally compact groups. Our approach applies to large classes of uniform approximate lattices (though not all of them) and is flexible enough to cover the L-p-versions of Property (FH) and a-(FH)-menability as well as quasified versions thereof a la Burger-Monod and Ozawa.
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| 3. |
- Björklund, Michael, 1981, et al.
(författare)
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Aperiodic order and spherical diffraction, I: auto-correlation of regular model sets
- 2018
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Ingår i: Proceedings of the London Mathematical Society. - : Wiley. - 0024-6115 .- 1460-244X. ; 116:4, s. 957-996
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Tidskriftsartikel (refereegranskat)abstract
- © 2017 London Mathematical Society We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as mathematical models of quasi-crystals. We then define a notion of auto-correlation for subsets of finite local complexitiy in arbitrary lcsc groups, which generalizes Hof's classical definition beyond the class of amenable groups, and prov ide a formula for the auto-correlation of a regular model set. Along the way we show that the punctured hull of an arbitrary regular model set admits a unique invariant probability measure, even in the case where the punctured hull is non-compact and the group is non-amenable. In fact this measure is also the unique stationary measure with respect to any admissible probability measure.
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| 4. |
- Björklund, Michael, 1981, et al.
(författare)
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Aperiodic order and spherical diffraction, II: translation bounded measures on homogeneous spaces
- 2021
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; In Press
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Tidskriftsartikel (refereegranskat)abstract
- We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone sets in (and even translation bounded measures on) arbitrary locally compact homogeneous metric spaces. We then specialize to the case of weighted model sets, in which we are able to derive more concrete formulas for the auto-correlation. In the case of Riemannian symmetric spaces we also explain how the auto-correlation of a weighted model set in a Riemannian symmetric space can be identified with a (typically non-tempered) positive-definite distribution on R-n. This paves the way for a diffraction theory for such model sets, which will be discussed in the sequel to the present article.
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| 5. |
- Björklund, Michael, 1981, et al.
(författare)
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Aperiodic order and spherical diffraction, III: The shadow transform and the diffraction formula
- 2021
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 281:12
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Tidskriftsartikel (refereegranskat)abstract
- We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of the hyperbolic plane we can interpret the spherical diffraction measure as the Mellin transform of the auto-correlation distribution. We show that uniform regular model sets in commutative spaces have a pure point spherical diffraction measure. The atoms of this measure are located at the spherical automorphic spectrum of the underlying lattice, and the diffraction coefficients can be characterized abstractly in terms of the so-called shadow transform of the characteristic functions of the window. In the case of the Heisenberg group we can give explicit formulas for these diffraction coefficients in terms of Bessel and Laguerre functions. (C) 2021 The Author(s). Published by Elsevier Inc.
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| 6. |
- Björklund, Michael, 1981, et al.
(författare)
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Approximate Invariance for Ergodic Actions of Amenable Groups
- 2019
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Ingår i: DISCRETE ANALYSIS. - : Alliance of Diamond Open Access Journals. - 2397-3129. ; 6, s. 56-
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Tidskriftsartikel (refereegranskat)abstract
- We develop in this paper some general techniques to analyze action sets of small doubling for probability measure-preserving actions of amenable groups. As an application of these techniques, we prove a dynamical generalization of Kneser's celebrated density theorem for subsets in (Z, +), valid for any countable amenable group, and we show how it can be used to establish a plethora of new inverse product set theorems for upper and lower asymptotic densities. We provide several examples demonstrating that our results are optimal for the settings under study.
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| 7. |
- Björklund, Michael, 1981, et al.
(författare)
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Approximate lattices
- 2018
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Ingår i: Duke Mathematical Journal. - : Duke University Press. - 0012-7094. ; 167:15, s. 2903-2964
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Tidskriftsartikel (refereegranskat)abstract
- In this article we introduce and study uniform and nonuniform approximate lattices in locally compact second countable (lcsc) groups. These are approximate subgroups (in the sense of Tao) which simultaneously generalize lattices in lcsc group and mathematical quasicrystals (Meyer sets) in lcsc Abelian groups. We show that envelopes of strong approximate lattices are unimodular and that approximate lattices in nilpotent groups are uniform. We also establish several results relating properties of approximate lattices and their envelopes. For example, we prove a version of the Milnor-Schwarz lemma for uniform approximate lattices in compactly generated lcsc groups, which we then use to relate the metric amenability of uniform approximate lattices to the amenability of the envelope. Finally we extend a theorem of Kleiner and Leeb to show that the isometry groups of irreducible higher-rank symmetric spaces of non-compact type are quasi-isometrically rigid with respect to finitely generated approximate groups.
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| 8. |
- Björklund, Michael, 1981, et al.
(författare)
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Bohr Sets in Triple Products of Large Sets in Amenable Groups
- 2019
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Ingår i: Journal of Fourier Analysis and Applications. - : Springer Science and Business Media LLC. - 1531-5851 .- 1069-5869. ; 25:3, s. 923-936
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Tidskriftsartikel (refereegranskat)abstract
- We answer a question of Hegyvári and Ruzsa concerning effective estimates of the Bohr-regularity of certain triple sums of sets with positive upper Banach densities in the integers. Our proof also works for any discrete amenable group, and it does not require all addends in the triple products we consider to have positive (left) upper Banach densities; one of the addends is allowed to only have positive upper asymptotic density with respect to a (possibly very sparse) ergodic sequence.
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| 9. |
- Björklund, Michael, 1981, et al.
(författare)
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BOREL DENSITY FOR APPROXIMATE LATTICES
- 2019
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Ingår i: Forum of Mathematics, Sigma. - : Cambridge University Press (CUP). - 2050-5094. ; 7
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Tidskriftsartikel (refereegranskat)abstract
- We extend classical density theorems of Borel and Dani-Shalom on lattices in semisimple, respectively solvable algebraic groups over local fields to approximate lattices. Our proofs are based on the observation that Zariski closures of approximate subgroups are close to algebraic subgroups. Our main tools are stationary joinings between the hull dynamical systems of discrete approximate subgroups and their Zariski closures.
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| 10. |
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