| 1. |
- Benjamini, I., et al.
(author)
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Visibility to infinity in the hyperbolic plane, despite obstacles
- 2009
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In: Latin American Journal of Probability and Mathematical Statistics. - 1980-0436. ; 6, s. 323-342
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Journal article (peer-reviewed)abstract
- Suppose that Z is a random closed subset of the hyperbolic plane H-2, whose law is invariant under isometrics of H-2. We prove that if the probability that Z contains a fixed ball of radius 1 is larger than some universal constant p0 < 1, then there is positive probability that Z contains (hi-infinite) lines. We then consider a family of random sets in H-2 that satisfy some additional natural assumptions. An example of such a set is the covered region in the Poisson Boolean model. Let f(r) be the probability that a line segment of length r is contained in such a set Z. We show that if f(r) decays fast enough, then there are as. no lines i Z. We also show that if the decay of f (r) is not too fast, then there are as. lines in Z. In the case of the Poisson Boolean model with balls of fixed radius R we characterize the critical intensity for the as. existence of lines in the covered region by an integral equation. We also determine when there are lines in the complement of a Poisson process on the space of lines in H-2.
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| 2. |
- Broman, Erik, 1977, et al.
(author)
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The existence phase transition for two Poisson random fractal models
- 2017
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In: Electronic Communications in Probability. - : Institute of Mathematical Statistics. - 1083-589X. ; 22
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Journal article (peer-reviewed)abstract
- In this paper we study the existence phase transition of the random fractal ball model and the random fractal box model. We show that both of these are in the empty phase at the critical point of this phase transition.
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| 3. |
- Jonasson, Lars S., 1983-, et al.
(author)
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Higher striatal D2-receptor availability in aerobically fit older adults but non-selective intervention effects after aerobic versus resistance training
- 2019
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In: NeuroImage. - : Elsevier. - 1053-8119 .- 1095-9572. ; 202
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Journal article (peer-reviewed)abstract
- There is much evidence that dopamine is vital for cognitive functioning in aging. Here we tested the hypothesis that aerobic exercise and fitness influence dopaminergic neurotransmission in the striatum, and in turn performance on offline working-memory updating tasks. Dopaminergic neurotransmission was measured by positron emission tomography (PET) and the non-displacable binding potential (BPND) of [11C]raclopride, i.e. dopamine (DA) D2-receptor (D2R) availability. Fifty-four sedentary older adults underwent a six-months exercise intervention, performing either aerobic exercise or stretching, toning, and resistance active control training. At baseline, higher aerobic fitness levels (VO2peak) were associated with higher BPND in the striatum, providing evidence of a link between an objective measure of aerobic fitness and D2R in older adults. BPND decreased substantially over the intervention in both groups but the intervention effects were non-selective with respect to exercise group. The decrease was several times larger than any previously estimated annual decline in D2R, potentially due to increased endogenous DA. Working-memory was unrelated to D2R both at baseline and following the intervention. To conclude, we provide partial evidence for a link between physical exercise and DA. Utilizing a PET protocol able to disentangle both D2R and DA levels could shed further light on whether, and how, aerobic exercise impacts the dopaminergic system in older adults.
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| 4. |
- Allerbo, Oskar, 1985, et al.
(author)
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Elastic Gradient Descent, an Iterative Optimization Method Approximating the Solution Paths of the Elastic Net
- 2023
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In: Journal of Machine Learning Research. - 1533-7928 .- 1532-4435. ; 24, s. 1-35
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Journal article (peer-reviewed)abstract
- The elastic net combines lasso and ridge regression to fuse the sparsity property of lasso with the grouping property of ridge regression. The connections between ridge regression and gradient descent and between lasso and forward stagewise regression have previously been shown. Similar to how the elastic net generalizes lasso and ridge regression, we introduce elastic gradient descent, a generalization of gradient descent and forward stagewise regression. We theoretically analyze elastic gradient descent and compare it to the elastic net and forward stagewise regression. Parts of the analysis are based on elastic gradient flow, a piecewise analytical construction, obtained for elastic gradient descent with infinitesimal step size. We also compare elastic gradient descent to the elastic net on real and simulated data and show that it provides similar solution paths, but is several orders of magnitude faster. Compared to forward stagewise regression, elastic gradient descent selects a model that, although still sparse, provides considerably lower prediction and estimation errors.
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| 5. |
- Brändén, Petter, et al.
(author)
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Negative dependence in sampling
- 2012
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In: Scandinavian Journal of Statistics. - : Wiley. - 0303-6898 .- 1467-9469. ; 39:4, s. 830-838
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Journal article (peer-reviewed)abstract
- The strong Rayleigh property is a new and robust negative dependence property that implies negative association; in fact it implies conditional negative association closed under external fields (CNA+). Suppose that and are two families of 0-1 random variables that satisfy the strong Rayleigh property and let . We show that {Zi} conditioned on is also strongly Rayleigh; this turns out to be an easy consequence of the results on preservation of stability of polynomials of Borcea & Branden (Invent. Math., 177, 2009, 521569). This entails that a number of important pps sampling algorithms, including Sampford sampling and Pareto sampling, are CNA+. As a consequence, statistics based on such samples automatically satisfy a version of the Central Limit Theorem for triangular arrays.
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| 6. |
- Deijfen, Maria, et al.
(author)
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Stationary random graphs on Z with prescribed iid degrees and finite mean connections
- 2006
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In: Electronic Communications in Probability. - 1083-589X. ; 11, s. 336-346
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Journal article (peer-reviewed)abstract
- Let F be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on Z with degree distribution F and it is shown for this model that the expected total length of all edges at a given vertex is finite if F has finite second moment. It is not hard to see that any stationary model for generating simple graphs on Z will give infinite mean for the total edge length per vertex if F does not have finite second moment. Hence, finite second moment of F is a necessary and sufficient condition for the existence of a model with finite mean total edge length.
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