Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time variable.Comment: 14 pages, to appea

Burial of a warrior of the Rouran period from Northern Altai

The article introduces into scientific discourse cultural, chronological and social interpretation of the warrior burial, investigated during the excavations of the necropolis of the Bulan-Koby Culture of the Choburak-I funerary and ritual complex. The site is located on the right bank of the Katun River, to the south from the Elanda village of Chemal district, Altai Republic. During the research, a burial of a man with a horse and accompanying equipment, including a representative set of weapons (bow, a large number of arrows with iron tips, a sword, two combat knives), a belt decorated with numerous belt fittings, horse equipment, and other items were studied. A detailed description of the finds, including both widespread and very rare types of items, has been carried out. The indicated circle of analogies from the sites of the Bulan-Koby Culture of Altai, as well as complexes excavated in adjacent territories, allows us to determine the date of burial mound №30 to the 4th c. AD. This conclusion is confirmed by the results of radiocarbon dating of a series of objects from the Choburak-I necropolis. The complex of elements of ritual practice indicates that the burial mound belongs to the previously identified Dialyan burial tradition of the Altai population of the end of the 1st mil. BC — first half of the 1st mil. AD. This is suggested by the combination of the following features: an oval mound with a crepidoma, inhumation burial rite, northwest orientation of the deceased, accompanying of the deceased by a horse laid “at the feet” of the person and its orientation with its head in the same direction as the deceased, inner grave construction in the form of a deck. The composition of the grave goods allows us to conclude that the buried man was of a high social status, possibly a warrior who commanded a large unit of professional warriors, and also, possibly, the leader of a local group of pastoralists who left the Choburak-I necropolis. Some peculiar features of the analysed complex reflect the ideological paradigm of the Bulan-Koby population, such as placement into the grave of a broken (disassembled?) bow and a large number of arrows, covering the person’s body at the time of the burial

Supplementary Material for: Autoimmune Disease-Associated Variants of Extracellular Endoplasmic Reticulum Aminopeptidase 1 Induce Altered Innate Immune Responses by Human Immune Cells

Endoplasmic reticulum aminopeptidase 1 <i>(ERAP1)</i> gene polymorphisms have been linked to several autoimmune diseases; however, the molecular mechanisms underlying these associations are not well understood. Recently, we demonstrated that ERAP1 regulates key aspects of the innate immune response. Previous studies show ERAP1 to be endoplasmic reticulum-localized and secreted during inflammation. Herein, we investigate the possible roles that ERAP1 polymorphic variants may have in modulating the innate immune responses of human peripheral blood mononuclear cells (hPBMCs) using two experimental methods: extracellular exposure of hPBMCs to ERAP1 variants and adenovirus (Ad)-based ERAP1 expression. We found that exposure of hPBMCs to ERAP1 variant proteins as well as ERAP1 overexpression by Ad5 vectors increased inflammatory cytokine and chemokine production, and enhanced immune cell activation. Investigating the molecular mechanisms behind these responses revealed that ERAP1 is able to activate innate immunity via multiple pathways, including the NLRP3 (NOD-like receptor, pyrin domain-containing 3) inflammasome. Importantly, these responses varied if autoimmune disease-associated variants of ERAP1 were examined in the assay systems. Unexpectedly, blocking ERAP1 cellular internalization augmented IL-1β production. To our knowledge, this is the first report identifying ERAP1 as being involved in modulating innate responses of human immune cells, a finding that may explain why ERAP1 has been genetically associated with several autoimmune diseases