Pathologies of the Brauer-Manin obstruction

We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the \'etale Brauer-Manin obstruction. We also give simple examples of threefolds with the same property that are families of 2-dimensional quadrics, and discuss some other examples and general properties of the Brauer-Manin obstruction.Comment: 22 pages, to appear in Mathematische Zeitschrif

Hyperon--anti-hyperon polarization asymmetry in relativistic heavy-ion collisions as an interplay between chiral and helical vortical effects

We argue that the enhancement in the spin polarization of anti-hyperons compared to the polarization of the hyperons in noncentral relativistic heavy-ion collisions arises as a result of an interplay between the chiral and helical vortical effects. The chiral vortical effect generates the axial current of quarks along the vorticity axis while the recently found helical vortical effect generates the helicity flow -- the projection of the quark's polarization vector onto its momentum -- along the same axis. For massless fermions, the helical charge corresponds to a difference in the contributions of particles and anti-particles to the axial charge. Assuming that the spin of light quarks transfers to the strange quarks via the vector kaon states ("the spin-vector dominance"), we are able to describe the ratio of the (anti)hyperon spin polarizations, obtained by the STAR group, without fitting parameters. We also argue that the helical vortical effect dominates over the chiral vortical effect and the chiral magnetic effect in the generation of the electric current.Comment: 9 pages, 3 figures; v2: discussions expanded, chiral magnetic effect and helical vortical effect are compare

Regulation of TRPC6 ion channels in podocytes — Implications for focal segmental glomerulosclerosis and acquired forms of proteinuric diseases

The glomerular filtration barrier is a highly specialized tri-layer structure with unique functional properties. Podocyte dysfunction and cytoskeletal disorganization leads to disruption of the slit diaphragma, and proteinuria. Inflammatory diseases involving the kidney as well as inherited podocytopathies or diabetic nephropathy cause injury of the podocyte network. Focal segmental glomerulosclerosis (FSGS) is a pathologic entity that is a common cause of nephrotic syndrome with severe proteinuria in both adults and children. Several causative genes have been identified in the pathogenesis of FSGS. Mutations of the transient receptor potential canonical-6 (TRPC6), a non-selective cation channel that is directly activated by diacylglycerol (DAG), cause a particularly aggressive form of FSGS. Angiotensin II, acting through its AT1 receptor, plays a critical role in generation of proteinuria and progression of kidney injury in a number of kidney diseases, including FSGS. Mounting evidence suggest the central role of TRPC6 and perhaps other TRPC channels in the pathogenesis of FSGS as well as of acquired forms of proteinuria such as diabetic nephropathy or hypertension. Identification of signaling pathways downstream of TRPC6 may provide novel targets for the treatment of proteinuria and prevent progression of podocyte injury

On Helly numbers of exponential lattices

Given a set S⊆R2S⊆R2, define the Helly number of SS, denoted by H(S)H(S), as the smallest positive integer NN, if it exists, for which the following statement is true: For any finite family FF of convex sets in~R2R2 such that the intersection of any NN or fewer members of~FF contains at least one point of SS, there is a point of SS common to all members of FF. We prove that the Helly numbers of exponential lattices {αn ⁣:n∈N0}2{αn:n∈N0​}2 are finite for every α>1α>1 and we determine their exact values in some instances. In particular, we obtain H({2n ⁣:n∈N0}2)=5H({2n:n∈N0​}2)=5, solving a problem posed by Dillon (2021). For real numbers α,β>1α,β>1, we also fully characterize exponential lattices L(α,β)={αn ⁣:n∈N0}×{βn ⁣:n∈N0}L(α,β)={αn:n∈N0​}×{βn:n∈N0​} with finite Helly numbers by showing that H(L(α,β))H(L(α,β)) is finite if and only if log⁡α(β)logα​(β) is rational

The STRANDS project: long-term autonomy in everyday environments

Thanks to the efforts of the robotics and autonomous systems community, the myriad applications and capacities of robots are ever increasing. There is increasing demand from end users for autonomous service robots that can operate in real environments for extended periods. In the Spatiotemporal Representations and Activities for Cognitive Control in Long-Term Scenarios (STRANDS) project (http://strandsproject.eu), we are tackling this demand head-on by integrating state-of-the-art artificial intelligence and robotics research into mobile service robots and deploying these systems for long-term installations in security and care environments. Our robots have been operational for a combined duration of 104 days over four deployments, autonomously performing end-user-defined tasks and traversing 116 km in the process. In this article, we describe the approach we used to enable long-term autonomous operation in everyday environments and how our robots are able to use their long run times to improve their own performance

Quadruplex DNA: sequence, topology and structure.

G-quadruplexes are higher-order DNA and RNA structures formed from G-rich sequences that are built around tetrads of hydrogen-bonded guanine bases. Potential quadruplex sequences have been identified in G-rich eukaryotic telomeres, and more recently in non-telomeric genomic DNA, e.g. in nuclease-hypersensitive promoter regions. The natural role and biological validation of these structures is starting to be explored, and there is particular interest in them as targets for therapeutic intervention. This survey focuses on the folding and structural features on quadruplexes formed from telomeric and non-telomeric DNA sequences, and examines fundamental aspects of topology and the emerging relationships with sequence. Emphasis is placed on information from the high-resolution methods of X-ray crystallography and NMR, and their scope and current limitations are discussed. Such information, together with biological insights, will be important for the discovery of drugs targeting quadruplexes from particular genes

Characterization of a K+-induced conformational switch in a human telomeric DNA oligonucleotide using 2-aminopurine fluorescence

Human telomeric DNA consists of tandem repeats of the DNA sequence d(GGGTTA). Oligodeoxynucletotide telomere models such as d[A(GGGTTA)(3)GGG] (Tel22) fold in a cation-dependent manner into quadruplex structures consisting of stacked G-quartets linked by d(TTA) loops. NMR has shown that in Na(+) solutions Tel22 forms a ‘basket’ topology of four antiparallel strands; in contrast, Tel22 in K(+) solutions consists of a mixture of unknown topologies. Our previous studies on the mechanism of folding of Tel22 and similar telomere analogs utilized changes in UV absorption between 270 and 325 nm that report primarily on G-quartet formation and stacking showed that quadruplex formation occurs within milliseconds upon mixing with an appropriate cation. In the current study, we assessed the dynamics and equilibria of folding of specific loops by using Tel22 derivatives in which the dA residues were serially substituted with the fluorescent reporter base, 2-aminopurine (2-AP). Tel22 folding induced by Na(+) or K(+) assessed by changes in 2-AP fluorescence consists of at least three kinetic steps with time constants spanning a range of ms to several hundred seconds. Na(+)-dependent equilibrium titrations of Tel22 folding could be approximated as a cooperative two-state process. In contrast, K(+)-dependent folding curves were biphasic, revealing that different conformational ensembles are present in 1 mM and 30 mM K(+). This conclusion was confirmed by (1)H NMR. Molecular dynamics simulations revealed a K(+) binding pocket in Tel22 located near dA1 that is specific for the so-called hybrid-1 conformation in which strand 1 is in a parallel arrangement. The possible presence of this topologically specific binding site suggests that K(+) may play an allosteric role in regulating telomere conformation and function by modulating quadruplex tertiary structure