Convergence of the all-time supremum of a L\'evy process in the heavy-traffic regime

In this paper we derive a technique of obtaining limit theorems for suprema of L\'evy processes from their random walk counterparts. For each $a>0$, let $\{Y^{(a)}_n:n\ge 1\}$ be a sequence of independent and identically distributed random variables and $\{X^{(a)}_t:t\ge 0\}$ be a L\'evy processes such that $X_1^{(a)}\stackrel{d}{=} Y_1^{(a)}$, $\mathbb E X_1^{(a)}<0$ and $\mathbb E X_1^{(a)}\uparrow0$ as $a\downarrow0$. Let $S^{(a)}_n=\sum_{k=1}^n Y^{(a)}_k$. Then, under some mild assumptions, $\Delta(a)\max_{n\ge 0} S_n^{(a)}\stackrel{d}{\to} R\iff\Delta(a)\sup_{t\ge 0} X^{(a)}_t\stackrel{d}{\to} R$, for some random variable $R$ and some function $\Delta(\cdot)$. We utilize this result to present a number of limit theorems for suprema of L\'evy processes in the heavy-traffic regime

Propolis Induces Chondroitin/Dermatan Sulphate and Hyaluronic Acid Accumulation in the Skin of Burned Wound

Changes in extracellular matrix glycosaminoglycans during the wound repair allowed us to apply the burn model in which therapeutic efficacy of propolis and silver sulfadiazine was compared. Burns were inflicted on four pigs. Glycosaminoglycans isolated from healthy and burned skin were quantified using a hexuronic acid assay, electrophoretic fractionation, and densitometric analyses. Using the reverse-phase HPLC the profile of sulfated disaccharides released by chondroitinase ABC from chondroitin/dermatan sulfates was estimated. Chondroitin/dermatan sulfates and hyaluronic acid were found in all samples. Propolis stimulated significant changes in the content of particular glycosaminoglycan types during burn healing. Glycosaminoglycans alterations after silver sulfadiazine application were less expressed. Propolis maintained high contribution of 4-O-sulfated disaccharides to chondroitin/dermatan sulfates structure and low level of 6-O-sulfated ones throughout the observed period of healing. Propolis led to preservation of significant contribution of disulfated disaccharides especially 2,4-O-disulfated ones to chondroitin sulfates/dermatan sulfates structure throughout the observed period of healing. Our findings demonstrate that propolis accelerates the burned tissue repair by stimulation of the wound bed glycosaminoglycan accumulation needed for granulation, tissue growth, and wound closure. Moreover, propolis accelerates chondroitin/dermatan sulfates structure modification responsible for binding growth factors playing the crucial role in the tissue repair

Gaussian queues in light and heavy traffic

In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\equiv\{X(t):t\in\mathbb R\}$ with stationary increments and variance function $\sigma^2_X(\cdot)$, equipped with a deterministic drift $c>0$, reflected at 0: $$Q_X^{(c)}(t)=\sup_{-\infty<s\le t}(X(t)-X(s)-c(t-s)).$$ We study the resulting stationary workload process $Q^{(c)}_X\equiv\{Q_X^{(c)}(t):t\ge0\}$ in the limiting regimes $c\to 0$ (heavy traffic) and $c\to\infty$ (light traffic). The primary contribution is that we show for both limiting regimes that, under mild regularity conditions on the variance function, there exists a normalizing function $\delta(c)$ such that $Q^{(c)}_X(\delta(c)\cdot)/\sigma_X(\delta(c))$ converges to a non-trivial limit in $C[0,\infty)$

n-3 Fatty Acid Supplementation for the Treatment of Dry Eye Disease.

BackgroundDry eye disease is a common chronic condition that is characterized by ocular discomfort and visual disturbances that decrease quality of life. Many clinicians recommend the use of supplements of n-3 fatty acids (often called omega-3 fatty acids) to relieve symptoms.MethodsIn a multicenter, double-blind clinical trial, we randomly assigned patients with moderate-to-severe dry eye disease to receive a daily oral dose of 3000 mg of fish-derived n-3 eicosapentaenoic and docosahexaenoic acids (active supplement group) or an olive oil placebo (placebo group). The primary outcome was the mean change from baseline in the score on the Ocular Surface Disease Index (OSDI; scores range from 0 to 100, with higher scores indicating greater symptom severity), which was based on the mean of scores obtained at 6 and 12 months. Secondary outcomes included mean changes per eye in the conjunctival staining score (ranging from 0 to 6) and the corneal staining score (ranging from 0 to 15), with higher scores indicating more severe damage to the ocular surface, as well as mean changes in the tear break-up time (seconds between a blink and gaps in the tear film) and the result on Schirmer's test (length of wetting of paper strips placed on the lower eyelid), with lower values indicating more severe signs.ResultsA total of 349 patients were assigned to the active supplement group and 186 to the placebo group; the primary analysis included 329 and 170 patients, respectively. The mean change in the OSDI score was not significantly different between the active supplement group and the placebo group (-13.9 points and -12.5 points, respectively; mean difference in change after imputation of missing data, -1.9 points; 95% confidence interval [CI], -5.0 to 1.1; P=0.21). This result was consistent across prespecified subgroups. There were no significant differences between the active supplement group and the placebo group in mean changes from baseline in the conjunctival staining score (mean difference in change, 0.0 points; 95% CI, -0.2 to 0.1), corneal staining score (0.1 point; 95% CI, -0.2 to 0.4), tear break-up time (0.2 seconds; 95% CI, -0.1 to 0.5), and result on Schirmer's test (0.0 mm; 95% CI, -0.8 to 0.9). At 12 months, the rate of adherence to treatment in the active supplement group was 85.2%, according to the level of n-3 fatty acids in red cells. Rates of adverse events were similar in the two trial groups.ConclusionsAmong patients with dry eye disease, those who were randomly assigned to receive supplements containing 3000 mg of n-3 fatty acids for 12 months did not have significantly better outcomes than those who were assigned to receive placebo. (Funded by the National Eye Institute, National Institutes of Health; DREAM ClinicalTrials.gov number, NCT02128763 .)

New Strategy for Rapid Diagnosis and Characterization of Fungal Infections: The Example of Corneal Scrapings

PURPOSE: The prognosis of people infected with Fungi especially immunocompromised depends on rapid and accurate diagnosis to capitalize on time administration of specific treatments. However, cultures produce false negative results and nucleic-acid amplification techniques require complex post-amplification procedures to differentiate relevant fungal types. The objective of this work was to develop a new diagnostic strategy based on real-time polymerase-chain reaction high-resolution melting analysis (PCR-HRM) that a) detects yeasts and filamentous Fungi, b) differentiates yeasts from filamentous Fungi, and c) discriminates among relevant species of yeasts. METHODS: PCR-HRM detection limits and specificity were assessed with a) isolated strains; b) human blood samples experimentally infected with Fungi; c) blood experimentally infected with other infectious agents; d) corneal scrapings from patients with suspected fungal keratitis (culture positive and negative) and e) scrapings from patients with suspected bacterial, viral or Acanthamoeba infections. The DNAs were extracted and mixed with primers diluted in the MeltDoctor® HRM Master Mix in 2 tubes, the first for yeasts, containing the forward primer CandUn (5'CATGCCTGTTTGAGCGTC) and the reverse primer FungUn (5'TCCTCCGCTT ATTGATATGCT) and the second for filamentous Fungi, containing the forward primer FilamUn (5'TGCCTGTCCGAGCGTCAT) and FungUn. Molecular probes were not necessary. The yields of DNA extraction and the PCR inhibitors were systematically monitored. RESULTS: PCR-HRM detected 0.1 Colony Forming Units (CFU)/µl of yeasts and filamentous Fungi, differentiated filamentous Fungi from yeasts and discriminated among relevant species of yeasts. PCR-HRM performances were higher than haemoculture and sensitivity and specificity was 100% for culture positive samples, detecting and characterizing Fungi in 7 out 10 culture negative suspected fungal keratitis. CONCLUSIONS: PCR-HRM appears as a new, sensitive, specific and inexpensive test that detects Fungi and differentiates filamentous Fungi from yeasts. It allows direct fungal detection from clinical samples and experimentally infected blood in less than 2.30 h after DNA extraction

A multi-ethnic genome-wide association study implicates collagen matrix integrity and cell differentiation pathways in keratoconus

Keratoconus is characterised by reduced rigidity of the cornea with distortion and focal thinning that causes blurred vision, however, the pathogenetic mechanisms are unknown. It can lead to severe visual morbidity in children and young adults and is a common indication for corneal transplantation worldwide. Here we report the first large scale genome-wide association study of keratoconus including 4,669 cases and 116,547 controls. We have identified significant association with 36 genomic loci that, for the first time, implicate both dysregulation of corneal collagen matrix integrity and cell differentiation pathways as primary disease-causing mechanisms. The results also suggest pleiotropy, with some disease mechanisms shared with other corneal diseases, such as Fuchs endothelial corneal dystrophy. The common variants associated with keratoconus explain 12.5% of the genetic variance, which shows potential for the future development of a diagnostic test to detect susceptibility to disease

Active heave compensation in offshore equipment with a neural network based control system

W artykule przedstawiono przykładowe rozwiązanie układu kompensującego ruchy statku wywołane falowaniem morskim. Zastosowano sterowanie w układzie zamkniętym, wykorzystując przy tym sztuczne sieci neuronowe. W analizowanym systemie lina jest prowadzona z wciągarki umiejscowionej na pokładzie jednostki, poprzez system krążków na A-ramie. Kompensacja ruchów statku bądź platformy umożliwia precyzyjne umieszczanie ładunku na dnie morza. Głównym komponentem odpowiedzialnym za eliminację ruchu ładunku jest system AHC wykorzystujący specjalny siłownik poruszający krążki i zmieniający długość liny. Zaproponowano prosty model umożliwiający symulacje układu w warunkach falowania oraz przeprowadzono przykładowe obliczenia.An offshore equipment with heave compensation system is presented in the paper. A simplified mathematical model allows studying the motion of the load when lowering towards seabed. During wavy sea, the load oscillations generated by a moving base (vessel, platform) make it very difficult to install a subsea unit on the seabed. Costly equipment has to be treated in a special way: an AHC system must be used in order to prevent the modules from damage. An example system presented is based on an A-frame, mounted in mid-ship over the moon pool and a winch system. In-line mounted compensator on the cross beam is considered. The rope length is controlled by application of a set of moving sheaves. Lagrange equations of the second order are applied in order to derive the equations of motion. The load is assumed to be a point mass, having three degrees of freedom. The rope model takes into account stiffness and damping. Motion of the vessel is assumed to be known. Dynamic optimisation enabling determination of the drive functions is defined. The optimal drive function realises the desired motion of the compensation cylinder, which minimises the load movement. Even for a simple and very efficient model, it is not possible to find an optimal course of AHC cylinder stroke in real-time. Therefore the optimisation is used further to generate a set of basic functions minimising the load movement for a defined weather window. A neural network is introduced, having used the generated base as learning data for the network teaching process. Then the neural network can be applied to simulations as an open loop controller, thanks to generalisation properties of the network. In order to improve the quality of compensation, a closed loop control system composed of a digital PID controller and the neural network is applied. Some numerical results are presented. The method de-scribed can be used in real-time, thus it is possible to implement it in practice