Diffraction of Return Time Measures Kesseböhmer, M.; Mosbach, A.; Samuel, T. ...
Journal of statistical physics,
02/2019, Volume:
174, Issue:
3
Journal Article
Peer reviewed
Open access
Letting
T
denote an ergodic transformation of the unit interval and letting
f
:
0
,
1
)
→
R
denote an observable, we construct the
f
-weighted return time measure
μ
y
for a reference point
y
∈
0
,
...1
)
as the weighted Dirac comb with support in
Z
and weights
f
∘
T
z
(
y
)
at
z
∈
Z
,
and if
T
is non-invertible, then we set the weights equal to zero for all
z
<
0
.
Given such a Dirac comb, we are interested in its diffraction spectrum and analyse it for the dependence on the underlying transformation. Under certain regularity conditions imposed on the interval map and the observable we explicitly calculate the diffraction of
μ
y
which consists of a trivial atom and an absolutely continuous part, almost surely with respect to
y
.
This contrasts what occurs in the setting of regular model sets arising from cut and project schemes and deterministic incommensurate structures. As a prominent example of non-mixing transformations, we consider rigid rotations. In this situation we observe that the diffraction of
μ
y
is pure point, almost surely with respect to
y
and, if the rotation number is irrational and the observable is Riemann integrable, then the diffraction of
μ
y
is independent of
y
.
Finally, for a converging sequence of rotation numbers, we provide new results concerning the limiting behaviour of the associated diffractions.
Regularity of aperiodic minimal subshifts Dreher, F.; Kesseböhmer, M.; Mosbach, A. ...
Bulletin of Mathematical Sciences,
12/2018, Volume:
8, Issue:
3
Journal Article
Peer reviewed
Open access
At the turn of this century Durand, and Lagarias and Pleasants established that key features of minimal subshifts (and their higher-dimensional analogues) to be studied are linearly repetitive, ...repulsive and power free. Since then, generalisations and extensions of these features, namely
α
-repetitive,
α
-repulsive and
α
-finite (
α
≥
1
), have been introduced and studied. We establish the equivalence of
α
-repulsive and
α
-finite for general subshifts over finite alphabets. Further, we studied a family of aperiodic minimal subshifts stemming from Grigorchuk’s infinite 2-group
G
. In particular, we show that these subshifts provide examples that demonstrate
α
-repulsive (and hence
α
-finite) is not equivalent to
α
-repetitive, for
α
>
1
. We also give necessary and sufficient conditions for these subshifts to be
α
-repetitive, and
α
-repulsive (and hence
α
-finite). Moreover, we obtain an explicit formula for their complexity functions from which we deduce that they are uniquely ergodic.
The grey mould fungus Botrytis cinerea causes losses of commercially important fruits, vegetables and ornamentals worldwide. Fungicide treatments are effective for disease control, but bear the risk ...of resistance development. The major resistance mechanism in fungi is target protein modification resulting in reduced drug binding. Multiple drug resistance (MDR) caused by increased efflux activity is common in human pathogenic microbes, but rarely described for plant pathogens. Annual monitoring for fungicide resistance in field isolates from fungicide-treated vineyards in France and Germany revealed a rapidly increasing appearance of B. cinerea field populations with three distinct MDR phenotypes. All MDR strains showed increased fungicide efflux activity and overexpression of efflux transporter genes. Similar to clinical MDR isolates of Candida yeasts that are due to transcription factor mutations, all MDR1 strains were shown to harbor activating mutations in a transcription factor (Mrr1) that controls the gene encoding ABC transporter AtrB. MDR2 strains had undergone a unique rearrangement in the promoter region of the major facilitator superfamily transporter gene mfsM2, induced by insertion of a retrotransposon-derived sequence. MDR2 strains carrying the same rearranged mfsM2 allele have probably migrated from French to German wine-growing regions. The roles of atrB, mrr1 and mfsM2 were proven by the phenotypes of knock-out and overexpression mutants. As confirmed by sexual crosses, combinations of mrr1 and mfsM2 mutations lead to MDR3 strains with higher broad-spectrum resistance. An MDR3 strain was shown in field experiments to be selected against sensitive strains by fungicide treatments. Our data document for the first time the rising prevalence, spread and molecular basis of MDR populations in a major plant pathogen in agricultural environments. These populations will increase the risk of grey mould rot and hamper the effectiveness of current strategies for fungicide resistance management.
The combination of carbidopa and levodopa (Sinemet) is a highly effective treatment for the symptoms of Parkinson's disease. However, side effects, such as abnormal involuntary movements, ...fluctuations in motor performance, and "wearing off" phenomena limit its long-term usefulness in some patients. Open-label studies show that controlled-release Sinemet CR is effective in reducing motor fluctuations. This report discusses the results of a 14-week double-blind crossover study comparing the efficacy and tolerability of standard Sinemet with controlled-release Sinemet CR. Overall, there were no statistically significant differences in efficacy between Sinemet CR and standard Sinemet on any of the major efficacy measures, suggesting a clinical equivalence in terms of treating the symptoms of Parkinson's disease. The study also supports the tolerability of Sinemet CR. In summary, Sinemet CR holds the promise of reducing some disturbing side effects of long-term levodopa therapy, thus achieving optimal control of parkinsonian symptoms.
For a long time, the treatment of retroperitoneal abscesses was exclusively surgical. Ultrasonography and computed tomography provide new therapeutic approaches to these lesions. The authors report a ...series of 17 renal and retroperitoneal abscesses treated by primary percutaneous drainage. This treatment generally ensures a favourable course, avoiding the need for surgery, which is still indicated in patients with associated uropathy or after failure of percutaneous drainage.
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