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- Ruge, Toralph, et al.
(författare)
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Circulating plasma levels of cathepsin S and L are not associated with disease severity in patients with rheumatoid arthritis
- 2014
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Ingår i: Scandinavian Journal of Rheumatology. - : Informa UK Limited. - 0300-9742 .- 1502-7732. ; 43:2, s. 371-373
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Tidskriftsartikel (refereegranskat)abstract
- Background: Rheumatoid arthritis (RA) is characterized by chronic synovitis and articular cartilage destruction. Increased activities of cathepsin S and cathepsin L, two potent cysteine proteases, are thought to play a role in the pathogenesis of the irreversible articular cartilage destruction. Nevertheless, data regarding the potential importance of the cathepsins as circulating biomarkers in RA patients are limited.Method: Subjects enrolled in this study are part of a larger study where patients from the three northern counties of Sweden diagnosed with early RA are followed in an ongoing prospective study. In total, 71 patients were included, along with 44 age- and sex-matched control subjects. Plasma levels of cathepsin S and L were analysed. Disease severity was assessed using the 28-joint count Disease Activity Score (DAS28).Results: Plasma levels of cathepsin S and L were significantly increased in patients with RA compared to healthy controls (p < 0.05 for both). However, in the patients with RA, no association between the cathepsins and the severity of the disease, as characterized by DAS28, was observed (p > 0.51).Conclusions: Although circulating levels of cathepsin S and L were significantly increased in patients with recently diagnosed RA, our data do not support the notion that circulating levels of cathepsins are relevant biomarkers for disease severity.
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- Södergren, Anders
(författare)
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Asymptotic Problems on Homogeneous Spaces
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This PhD thesis consists of a summary and five papers which all deal with asymptotic problems on certain homogeneous spaces. In Paper I we prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. All our results are given with precise estimates on the rates of convergence to equidistribution. Papers II and III are concerned with statistical problems on the space of n-dimensional lattices of covolume one. In Paper II we study the distribution of lengths of non-zero lattice vectors in a random lattice of large dimension. We prove that these lengths, when properly normalized, determine a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. In Paper III we complement this result by proving that the asymptotic distribution of the angles between the shortest non-zero vectors in a random lattice is that of a family of independent Gaussians. In Papers IV and V we investigate the value distribution of the Epstein zeta function along the real axis. In Paper IV we determine the asymptotic value distribution and moments of the Epstein zeta function to the right of the critical strip as the dimension of the underlying space of lattices tends to infinity. In Paper V we determine the asymptotic value distribution of the Epstein zeta function also in the critical strip. As a special case we deduce a result on the asymptotic value distribution of the height function for flat tori. Furthermore, applying our results we discuss a question posed by Sarnak and Strömbergsson as to whether there in large dimensions exist lattices for which the Epstein zeta function has no zeros on the positive real line.
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- Södergren, Anders
(författare)
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On the distribution of angles between the N shortest vectors in a random lattice
- 2011
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 84:3, s. 749-764
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Tidskriftsartikel (refereegranskat)abstract
- We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n→∞. Moreover, we interpret the result in terms of eigenvalues and eigenfunctions of the Laplacian on flat tori. Finally, we discuss the limit distribution of any finite number of successive minima of a random n-dimensional lattice as n→∞.
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- Södergren, Anders
(författare)
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On the Poisson distribution of lengths of lattice vectors in a random lattice
- 2011
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 269:3-4, s. 945-954
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the volumes determined by the lengths of the non-zero vectors +/- x in a random lattice L of covolume 1 define a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. This generalizes earlier results by Rogers (Proc Lond Math Soc (3) 6:305-320, 1956, Thm. 3) and Schmidt (Acta Math 102: 159-224, 1959, Satz 10).
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- Södergren, Anders
(författare)
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On the uniform equidistribution of closed horospheres in hyperbolic manifolds
- 2012
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Ingår i: Proceedings of the London Mathematical Society. - : Wiley. - 0024-6115 .- 1460-244X. ; 105, s. 225-280
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Tidskriftsartikel (refereegranskat)abstract
- We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal ['On the uniform equidistribution of long closed horocycles', Loo-Keng Hua: a great mathematician of the twentieth century, Asian J. Math. 4 (2000) 839-853] and Strombergsson ['On the uniform equidistribution of long closed horocycles', Duke Math. J. 123 (2004) 507-547] in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.
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- Södergren, Anders
(författare)
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On the value distribution and moments of the Epstein zeta function to the right of the critical strip
- 2011
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Ingår i: Journal of Number Theory. - : Elsevier BV. - 0022-314X .- 1096-1658. ; 131:7, s. 1176-1208
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Tidskriftsartikel (refereegranskat)abstract
- We study the Epstein zeta function E-n(L, S) for s > n/2 and a random lattice L of large dimension n. For any fixed c > 1/2 we determine the value distribution and moments of E-n(., cn) (suitably normalized) as n -> infinity. We further discuss the random function C -> E-n(., cn) for c is an element of [A, B] with 1/2 < A < B and determine its limit distribution as n -> infinity.
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| 9. |
- Södergren, Anders
(författare)
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On The Value Distribution Of The Epstein Zeta Function In The Critical Strip
- 2013
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Ingår i: Duke mathematical journal. - : Duke University Press. - 0012-7094 .- 1547-7398. ; 162:1, s. 1-48
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Tidskriftsartikel (refereegranskat)abstract
- We study the value distribution of the Epstein zeta function E-n (L, s) for 0 infinity, we prove that the random variable V-n(-2c) E-n(.,cn) has a limit distribution, which we give explicitly (here V-n is the volume of the n-dimensional unit ball). More generally, for any fixed epsilon > 0, we determine the limit distribution of the random function c bar right arrow V-n(-2c) E-n(., cn), c epsilon [1/4 + epsilon, 1/2 - epsilon]. After compensating for the pole at c = 1/2, we even obtain a limit result on the whole interval [1/4 + epsilon, 1/2], and as a special case we deduce the following strengthening of a result by Sarnak and Strombergsson concerning the height function h(n) (L) of the flat torus R-n/L: the random variable n{h(n) (L) - (log(4 pi) - gamma + 1)} + log n has a limit distribution as n -> infinity, which we give explicitly. Finally, we discuss a question posed by Sarnak and Strombergsson as to whether there exists a lattice L subset of R-n for which E-n(L, s) has no zeros in (0, infinity).
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