Let
μ
N
be the empirical measure associated to a
N
-sample of a given probability distribution
μ
on
R
d
. We are interested in the rate of convergence of
μ
N
to
μ
, when measured in the Wasserstein ...distance of order
p
>
0
. We provide some satisfying non-asymptotic
L
p
-bounds and concentration inequalities, for any values of
p
>
0
and
d
≥
1
. We extend also the non asymptotic
L
p
-bounds to stationary
ρ
-mixing sequences, Markov chains, and to some interacting particle systems.
We are interested in the two-dimensional Keller–Segel partial differential equation. This equation is a model for chemotaxis (and for Newtonian gravitational interaction). When the total mass of the ...initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity χ of bacteria to the chemo-attractant is larger than 8π. We investigate its approximation by a system of N two-dimensional Brownian particles interacting through a singular attractive kernel in the drift term. In the very subcritical case χ < 2π, the diffusion strongly dominates this singular drift: we obtain existence for the particle system and prove that its flow of empirical measures converges, as N → ∞ and up to extraction of a subsequence, to a weak solution of the Keller–Segel equation. We also show that for any N ≥ 2 and any value of χ > 0, pairs of particles do collide with positive probability: the singularity of the drift is indeed visited. Nevertheless, when χ < 2π N, it is possible to control the drift and obtain existence of the particle system until the first time when at least three particles collide. We check that this time is a.s. infinite, so that global existence holds for the particle system, if and only if χ ≤ 8π(N – 2)/(N – 1). Finally, we remark that in the system with N = 2 particles, the difference between the two positions provides a natural two-dimensional generalization of Bessel processes, which we study in details.
We report herein the syntheses of original pyrazolines and pyrazoles through 1,3‐dipolar cycloaddition of cyclic enones with 2,5‐disubstituted nitrile imines achieved via photochemical activation of ...2,5‐diaryl substituted tetrazoles. Monitoring of the reactions, similar to nitrile imine‐mediated tetrazole‐ene cycloadditions (NITEC), could be performed by means of UV‐vis absorption and emission measurements. The presence or absence of substituents in the alpha position of the ketone function makes it possible to direct these reactions towards the selective formation of pyrazoles or pyrazolines. The choice of the cyclic enones and 2,5‐disubstituted tetrazoles proved crucial for the fluorescence properties of the polycyclic derivatives obtained.
1,3‐dipolar cycloaddition of cyclic enones with 2,5‐disubstituted nitrile‐imines obtained by photochemical activation of 2,5‐diaryl substituted tetrazoles leads to the formation of novel pyrazoles and pyrazolines. Reactions can be monitored using UV‐vis absorption and emission measurements.
We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order $\alpha$ with drift and diffusion coefficients $b,\sigma$. When $\alpha\in (1,2)$, we investigate ...pathwise uniqueness for this equation. When $\alpha\in (0,1)$, we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether $\alpha\in (0,1)$ or $\alpha \in (1,2)$ and on whether the driving stable process is symmetric or not. Our assumptions involve the regularity and monotonicity of $b$ and $\sigma$.
A high demand for seafood in combination with overfishing threatens living marine resources worldwide. Sound regulation and enforcement is needed for sustainable management, yet the seafood business ...is characterized by high levels of uncertainty regarding product identity. Here, 280 fish dishes sold in commercial restaurants, canteens of the European Union and sushi bars throughout Brussels, Belgium were assessed for mislabeling using DNA barcoding. Overall 31.1% mislabeled samples were detected, with mislabeling present in all types of vendors. Cod and sole were the most frequently sampled and were also mislabeled regularly (13.1% and 11.1%). Bluefin tuna was substituted almost always (95% mislabeling), mostly by other tuna species. Results show that seafood labeling rules and controls are not sufficient, particularly in the food service industry, where for example commercial denominations can be ambiguous and scientific species denomination is not compulsory. Irrespective if negligent or fraudulent, mislabeling practices are detrimental for economical and sustainability goals and also consumers' trust.
•280 samples of fish dishes were collected in Brussels and molecularly tested.•Mislabeling was present in cod (13.1%), sole (11.1%) and bluefin tuna (95.0%).•Bluefin tuna was substituted mostly by other tuna species.•The overall mislabeling rate was 31.1% and 38.1% in EU canteens.
The vulnerability of social-ecological systems in sub-Saharan Africa (SSA) to climate variability and change means that there is an urgent need to better integrate weather and climate information ...into societal decision-making processes. Long-term climate adaptation in these regions has received increasing attention, with recent initiatives aiming to increase resilience to climate change at timescales of years to decades. Less focus has been given to weather and short-term climate information. However, users are principally interested in shorter timescales (hours to seasons) where actions can immediately reduce the impacts of severe weather events. Focusing on the priority sectors of agriculture and food security, water and disaster management, this paper uses a systematic literature review approach to analyse 61 empirical case studies drawn from academic literature and projects across SSA. We identify the main users of climate services and outline current practices and reported benefits. Barriers that impede the delivery and uptake of climate services are identified and potential strategies for overcoming them outlined based on the reporting of successful practices. Our findings show that greater capacity building of personnel working for National Meteorological and Hydrological Services and Agricultural Extension staff and reinforcing and sustaining collaboration between different stakeholders (climate scientists, hydrologists, extension workers, farmers and other user groups), are essential factors for improving the uptake and utility of weather and climate services to enhance resilience to climate shocks in SSA.
We prove a quantitative result of convergence of a conservative stochastic particle system to the solution of the homogeneous Landau equation for hard potentials. There are two main difficulties: (i) ...the known stability results for this class of Landau equations concern regular solutions and seem difficult to extend to study the rate of convergence of some empirical measures; (ii) the conservativeness of the particle system is an obstacle for (approximate) independence. To overcome (i), we prove a new stability result for the Landau equation for hard potentials concerning very general measure solutions. Due to (ii), we have to couple, our particle system with some non independent nonlinear processes, of which the law solves, in some sense, the Landau equation. We then prove that these nonlinear processes are not so far from being independent. Using finally some ideas of Rousset 25, we show that in the case of Maxwell molecules, the convergence of the particle system is uniform in time.
Pain is a common symptom related to inflammatory bowel disease (IBD). In addition to abdominal pain, pain can also be an extraintestinal manifestation of IBD. Pain treatment is challenging and a ...substantial part of IBD patients are treated with opioids. Therefore, a better knowledge on pain symptoms is crucial for a better therapeutic approach to this clinical problem.
Patients of the Swiss IBD Cohort Study (SIBDCS) (n = 2152) received a questionnaire regarding pain intensity, pain localization and impact of pain on daily life and social activities. Furthermore, the questionnaire investigated the use of pain-specific medication.
A vast majority of patients (71%) experienced pain during the disease course. For a substantial part of patients (49% in UC and 55% in CD) pain is a longstanding problem (>5 years). Pain in UC was of shorter duration compared to CD (p < 0.01). Abdominal pain (59.5%) and back pain (38.3%) were the main pain localizations. 67% of patients took pain medication; 24% received no pain treatment. The general quality of life was significantly lower in patients suffering of pain compared to those without pain (38 vs. 77; (-100 very bad; 100 very good) p<0.0001).
Prevalence of pain is high in patients of the SIBDCS. It is a longstanding problem for the majority of the patients affected. Pain was found to be undertreated in the SIBDCS and was significantly associated with health-related quality of life. Thus, an increased awareness is mandatory to address this frequent complication in the course of IBD.
Data evaluating the chronological order of appearance of extraintestinal manifestations (EIMs) relative to the time of inflammatory bowel disease (IBD) diagnosis is currently lacking. We aimed to ...assess the type, frequency, and chronological order of appearance of EIMs in patients with IBD.
Data from the Swiss Inflammatory Bowel Disease Cohort Study were analyzed.
The data on 1249 patients were analyzed (49.8% female, median age: 40 interquartile range, 30-51 yr, 735 58.8% with Crohn's disease, 483 38.7% with ulcerative colitis, and 31 2.5% with indeterminate colitis). A total of 366 patients presented with EIMs (29.3%). Of those, 63.4% presented with 1, 26.5% with 2, 4.9% with 3, 2.5% with 4, and 2.7% with 5 EIMs during their lifetime. Patients presented with the following diseases as first EIMs: peripheral arthritis 70.0%, aphthous stomatitis 21.6%, axial arthropathy/ankylosing spondylitis 16.4%, uveitis 13.7%, erythema nodosum 12.6%, primary sclerosing cholangitis 6.6%, pyoderma gangrenosum 4.9%, and psoriasis 2.7%. In 25.8% of cases, patients presented with their first EIM before IBD was diagnosed (median time 5 mo before IBD diagnosis: range, 0-25 mo), and in 74.2% of cases, the first EIM manifested itself after IBD diagnosis (median: 92 mo; range, 29-183 mo).
In one quarter of patients with IBD, EIMs appeared before the time of IBD diagnosis. Occurrence of EIMs should prompt physicians to look for potential underlying IBD.
We consider the spatially homogeneous Boltzmann equation for hard potentials without cutoff. We prove that an exponential moment of order
ρ
=
min
{
2
γ
/
(
2
-
ν
)
,
2
}
, with the usual notation, is ...immediately created. This is stronger than what happens in the case with cutoff. We also show that exponential moments of order
ρ
∈
(
0
,
2
are propagated.
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