This paper is concerned with the incompressible Euler equations. In Onsager’s critical classes we provide explicit formulas for the Duchon–Robert measure in terms of the regularization kernel and a ...family of vector-valued measures
{
μ
z
}
z
⊂
M
x
,
t
, having some Hölder regularity with respect to the direction
z
∈
B
1
. Then, we prove energy conservation for
L
x
,
t
∞
∩
L
t
1
B
V
x
solutions, in both the absence or presence of a physical boundary. This result generalises the previously known case of Vortex Sheets, showing that energy conservation follows from the structure of
L
∞
∩
B
V
incompressible vector fields rather than the flow having “organized singularities”. The interior energy conservation features the use of Ambrosio’s anisotropic optimization of the convolution kernel and it differs from the usual energy conservation arguments by heavily relying on the incompressibility of the vector field. This is the first energy conservation proof, for a given class of solutions, which fails to simultaneously apply to both compressible and incompressible models, coherently with compressible shocks having non-trivial entropy production. To run the boundary analysis we introduce a notion of “normal Lebesgue trace” for general vector fields, very reminiscent of the one for
BV
functions. We show that having such a null normal trace is basically equivalent to have vanishing boundary energy flux. This goes beyond the previous approaches, laying down a setup which applies to every Lipschitz bounded domain. Allowing any Lipschitz boundary introduces several technicalities to the proof, with a quite geometrical/measure-theoretical flavour.
Human lactoferrin (hLf), an iron-binding multifunctional cationic glycoprotein secreted by exocrine glands and by neutrophils, is a key element of host defenses. HLf and bovine Lf (bLf), possessing ...high sequence homology and identical functions, inhibit bacterial growth and biofilm dependently from iron binding ability while, independently, bacterial adhesion to and the entry into cells. In infected/inflamed host cells, bLf exerts an anti-inflammatory activity against interleukin-6 (IL-6), thus up-regulating ferroportin (Fpn) and transferrin receptor 1 (TfR1) and down-regulating ferritin (Ftn), pivotal actors of iron and inflammatory homeostasis (IIH). Consequently, bLf inhibits intracellular iron overload, an unsafe condition enhancing in vivo susceptibility to infections, as well as anemia of inflammation (AI), re-establishing IIH. In pregnant women, affected by AI, bLf oral administration decreases IL-6 and increases hematological parameters. This surprising effect is unrelated to iron supplementation by bLf (80 μg instead of 1-2 mg/day), but to its role on IIH. AI is unrelated to the lack of iron, but to iron delocalization: cellular/tissue overload and blood deficiency. BLf cures AI by restoring iron from cells to blood through Fpn up-expression. Indeed, anti-inflammatory activity of oral and intravaginal bLf prevents preterm delivery. Promising bLf treatments can prevent/cure transitory inflammation/anemia/oral pathologies in athletes.
Lactoferrin (Lf), a cationic glycoprotein able to chelate two ferric irons per molecule, is synthesized by exocrine glands and neutrophils. Since the first anti-microbial function attributed to Lf, ...several activities have been discovered, including the relevant anti-inflammatory one, especially associated to the down-regulation of pro-inflammatory cytokines, as IL-6. As high levels of IL-6 are involved in iron homeostasis disorders, Lf is emerging as a potent regulator of iron and inflammatory homeostasis. Here, the role of Lf against aseptic and septic inflammation has been reviewed. In particular, in the context of aseptic inflammation, as anemia of inflammation, preterm delivery, Alzheimer's disease and type 2 diabetes, Lf administration reduces local and/or systemic inflammation. Moreover, Lf oral administration, by decreasing serum IL-6, reverts iron homeostasis disorders. Regarding septic inflammation occurring in
infection, cystic fibrosis and inflammatory bowel disease, Lf, besides the anti-inflammatory activity, exerts a significant activity against bacterial adhesion, invasion and colonization. Lastly, a critical analysis of literature in vitro data reporting contradictory results on the Lf role in inflammatory processes, ranging from pro- to anti-inflammatory activity, highlighted that they depend on cell models, cell metabolic status, stimulatory or infecting agents as well as on Lf iron saturation degree, integrity and purity.
Recently, the world has been dealing with a devastating global pandemic coronavirus infection, with more than 12 million infected worldwide and over 300,000 deaths as of May 15th 2020, related to a ...novel coronavirus (2019-nCoV), characterized by a spherical morphology and identified through next-generation sequencing. Although the respiratory tract is the primary portal of entry of SARS-CoV-2, gastrointestinal involvement associated with nausea, vomiting and diarrhoea may also occur. No drug or vaccine has been approved due to the absence of evidence deriving from rigorous clinical trials. Increasing interest has been highlighted on the possible preventative role and adjunct treatment of lactoferrin, glycoprotein of human secretions part of a non-specific defensive system, known to play a crucial role against microbial and viral infections and exerting anti-inflammatory effects on different mucosal surfaces and able to regulate iron metabolism. In this review, analysing lactoferrin properties, we propose designing a clinical trial to evaluate and verify its effect using a dual combination treatment with local, solubilized intranasal spray formulation and oral administration. Lactoferrin could counteract the coronavirus infection and inflammation, acting either as natural barrier of both respiratory and intestinal mucosa or reverting the iron disorders related to the viral colonization.
Despite recent advances in cancer therapy, current treatments, including radiotherapy, chemotherapy, and immunotherapy, although beneficial, present attendant side effects and long-term sequelae, ...usually more or less affecting quality of life of the patients. Indeed, except for most of the immunotherapeutic agents, the complete lack of selectivity between normal and cancer cells for radio- and chemotherapy can make them potential antagonists of the host anti-cancer self-defense over time. Recently, the use of nutraceuticals as natural compounds corroborating anti-cancer standard therapy is emerging as a promising tool for their relative abundance, bioavailability, safety, low-cost effectiveness, and immuno-compatibility with the host. In this review, we outlined the anti-cancer properties of Lactoferrin (Lf), an iron-binding glycoprotein of the innate immune defense. Lf shows high bioavailability after oral administration, high selectivity toward cancer cells, and a wide range of molecular targets controlling tumor proliferation, survival, migration, invasion, and metastasization. Of note, Lf is able to promote or inhibit cell proliferation and migration depending on whether it acts upon normal or cancerous cells, respectively. Importantly, Lf administration is highly tolerated and does not present significant adverse effects. Moreover, Lf can prevent development or inhibit cancer growth by boosting adaptive immune response. Finally, Lf was recently found to be an ideal carrier for chemotherapeutics, even for the treatment of brain tumors due to its ability to cross the blood-brain barrier, thus globally appearing as a promising tool for cancer prevention and treatment, especially in combination therapies.
A
bstract
We employ path integral methods to calculate the Casimir energy and force densities in a chiral extension of QED. Manifestly gauge invariant perfect electromagnetic boundary conditions, a ...natural generalization of perfect electric and perfect magnetic conditions, are implemented directly in the action by the usage of auxiliary fields. The chiral properties of the vacuum are modelled using a background
θ
field, and we introduce techniques to efficiently calculate the path integral in this chiral medium. The flexibility of our method allows us to naturally obtain results for a variety of configurations, and where comparison is possible our results are in perfect agreement with existing literature. Among these are multiple situations where a repulsive Casimir force is possible.
The innate defense system of the female mucosal genital tract involves a close and complex interaction among the healthy vaginal microbiota, different cells, and various proteins that protect the ...host from pathogens. Vaginal lactobacilli and lactoferrin represent two essential actors in the vaginal environment. Lactobacilli represent the dominant bacterial species able to prevent facultative and obligate anaerobes outnumber in vaginal microbiota maintaining healthy microbial homeostasis. Several mechanisms underlie the protection exerted by lactobacilli: competition for nutrients and tissue adherence, reduction of the vaginal pH, modulation of immunity, and production of bioactive compounds. Among bioactive factors of cervicovaginal mucosa, lactoferrin, an iron-binding cationic glycoprotein, is a multifunctional glycoprotein with antibacterial, antifungal, antiviral, and antiparasitic activities, recently emerging as an important modulator of inflammation. Lactobacilli and lactoferrin are largely under the influence of female hormones and of paracrine production of various cytokines. Lactoferrin is strongly increased in lower genital tract mucosal fluid of women affected by
, and
infections promoting both innate and adaptive immune responses. In vaginal dysbiosis characterized by low amounts of vaginal lactobacilli and increased levels of endogenous anaerobic bacteria, the increase in lactoferrin could act as an immune modulator assuming the role normally played by the healthy microbiota in vaginal mucosa. Then lactoferrin and lactobacilli may be considered as biomarkers of altered microbial homeostasis at vaginal level. Considering the shortage of effective treatments to counteract recurrent and/or antibiotic-resistant bacterial infections, the intravaginal administration of lactobacilli and lactoferrin could be a novel efficient therapeutic strategy and a valuable tool to restore mucosal immune homeostasis.
We revisit the path integral computation of the Casimir energy between two infinite parallel plates placed in a QED vacuum. We implement perfectly magnetic conductor boundary conditions (as a prelude ...to the dual superconductor picture of the QCD vacuum) via constraint fields and show how an effective gauge theory can be constructed for the constraint boundary fields, from which the Casimir energy can be simply computed, in perfect agreement with the usual more involved approaches. Gauge invariance is natural in this framework, as well as the generalization of the result to d dimensions. We also pay attention to the case where the outside of the plates is not the vacuum, but a perfect magnetic (super)conductor, disallowing any dynamics outside the plates. We find perfect agreement between both setups.
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