Algorithmic decidability of Engel's property for automaton groups

We consider decidability problems associated with Engel's identity ($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) in groups generated by an automaton. We give a partial algorithm that decides, given $x,y$, whether an Engel identity is satisfied. It succeeds, importantly, in proving that Grigorchuk's $2$-group is not Engel. We consider next the problem of recognizing Engel elements, namely elements $y$ such that the map $x\mapsto[x,y]$ attracts to $\{1\}$. Although this problem seems intractable in general, we prove that it is decidable for Grigorchuk's group: Engel elements are precisely those of order at most $2$. Our computations were implemented using the package FR within the computer algebra system GAP

New High Field State of Flux Line Lattice in Unconventional Superconductor CeCoIn_5

Ultrasound velocity measurements of the unconventional superconductor CeCoIn_5 with extremely large Pauli paramagnetic susceptibility reveal an unusual structural transformation of the flux line lattice (FLL) in the vicinity of the upper critical field. The transition field coincides with that at which heat capacity measurements reveal a second order phase transition. The lowering of the sound velocity at the transition is consistent with the collapse of the FLL tilt modulus and a crossover to quasi two-dimensional FLL pinning. These results provide a strong evidence that the high field state is the Fulde-Ferrel-Larkin-Ovchinikov phase, in which the order parameter is spatially modulated and has planar nodes aligned perpendicular to the vortices.Comment: 5 pages, 4 figure

Late Endosomal Cholesterol Accumulation Leads to Impaired Intra-Endosomal Trafficking

Background Pathological accumulation of cholesterol in late endosomes is observed in lysosomal storage diseases such as Niemann-Pick type C. We here analyzed the effects of cholesterol accumulation in NPC cells, or as phenocopied by the drug U18666A, on late endosomes membrane organization and dynamics. Methodology/Principal Findings Cholesterol accumulation did not lead to an increase in the raft to non-raft membrane ratio as anticipated. Strikingly, we observed a 2–3 fold increase in the size of the compartment. Most importantly, properties and dynamics of late endosomal intralumenal vesicles were altered as revealed by reduced late endosomal vacuolation induced by the mutant pore-forming toxin ASSP, reduced intoxication by the anthrax lethal toxin and inhibition of infection by the Vesicular Stomatitis Virus. Conclusions/Significance These results suggest that back fusion of intralumenal vesicles with the limiting membrane of late endosomes is dramatically perturbed upon cholesterol accumulation

Conventional Magnetic Superconductors: Coexistence of Singlet Superconductivity and Magnetic Order

The basic physics of bulk magnetic superconductors (MS) related to the problem of the coexistence of singlet superconductivity (SC) and magnetic order is reviewed. The interplay between exchange (EX) and electromagnetic (EM) interaction is discussed and argued that the singlet SC and uniform ferromagnetic (F) order practically never coexist. In case of their mutual coexistence the F order is modified into a domain-like or spiral structure depending on magnetic anisotropy. It turns out that this situation is realized in several superconductors such as $ErRh_{4}B_{4}$, $HoMo_{6}S_{8}$, $HoMo_{6}Se_{8}$ with electronic and in $AuIn_{2}$ with nuclear magnetic order. The later problem is also discussed here. The coexistence of SC and antiferromagnetism is more favorable than with the modified F order. Very interesting physics is realized in systems with SC and weak-ferromagnetism which results in an very reach phase diagram. The properties of magnetic superconductors in magnetic field are very peculiar, especially near the (ferro)magnetic transition temperature where the upper critical field becomes smaller than the thermodynamical critical field. The extremely interesting physics of Josephson junctions based on MS with spiral magnetic order is also discussed. The existence of the triplet pairing amplitude $F_{\uparrow \uparrow}$ ($F_{\downarrow \downarrow}$) in MS with rotating magnetization (the effect recently rediscovered in SFS junctions) gives rise to the so called $\pi$-contact. Furthermore, the interplay of the superconducting and magnetic phase in such a contact renders possibilities for a new type of coupled Josephson-qubits.Comment: 28 pages, 3 figures; submitted for the Special Issue Comptes de l'Academie des Sciences: Problems of the Coexistence of Magnetism and Superconductivity, edited by A. Buzdi

Co-infection of the four major Plasmodium species: effects on densities and gametocyte carriage

BACKGROUND: Co-infection of the four major species of human malaria parasite Plasmodium falciparum (Pf), P. vivax (Pv), P. malariae (Pm), and P. ovale sp. (Po) is regularly observed, but there is limited understanding of between-species interactions. In particular, little is known about the effects of multiple Plasmodium species co-infections on gametocyte production. METHODS: We developed molecular assays for detecting asexual and gametocyte stages of Pf, Pv, Pm, and Po. This is the first description of molecular diagnostics for Pm and Po gametocytes. These assays were implemented in a unique epidemiological setting in Papua New Guinea with sympatric transmission of all four Plasmodium species permitting a comprehensive investigation of species interactions. FINDINGS: The observed frequency of Pf-Pv co-infection for asexual parasites (14.7%) was higher than expected from individual prevalence rates (23.8%Pf x 47.4%Pv = 11.3%). The observed frequency of co-infection with Pf and Pv gametocytes (4.6%) was higher than expected from individual prevalence rates (13.1%Pf x 28.2%Pv = 3.7%). The excess risk of co-infection was 1.38 (95% confidence interval (CI): 1.09, 1.67) for all parasites and 1.37 (95% CI: 0.95, 1.79) for gametocytes. This excess co-infection risk was partially attributable to malaria infections clustering in some villages. Pf-Pv-Pm triple infections were four times more frequent than expected by chance alone, which could not be fully explained by infections clustering in highly exposed individuals. The effect of co-infection on parasite density was analyzed by systematic comparison of all pairwise interactions. This revealed a significant 6.57-fold increase of Pm density when co-infected with Pf. Pm gametocytemia also increased with Pf co-infection. CONCLUSIONS: Heterogeneity in exposure to mosquitoes is a key epidemiological driver of Plasmodium co-infection. Among the four co-circulating parasites, Pm benefitted most from co-infection with other species. Beyond this, no general prevailing pattern of suppression or facilitation was identified in pairwise analysis of gametocytemia and parasitemia of the four species. TRIAL REGISTRATION: This trial is registered with ClinicalTrials.gov, Trial ID: NCT02143934

Temperature dependence of the upper critical field of an anisotropic singlet superconductivity in a square lattice tight-binding model in parallel magnetic fields

Upper critical field parallel to the conducting layer is studied in anisotropic type-II superconductors on square lattices. We assume enough separation of the adjacent layers, for which the orbital pair-breaking effect is suppressed for exactly aligned parallel magnetic field. In particular, we examine the temperature dependence of the critical field H_c(T) of the superconductivity including the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) state, in which the Cooper pairs have non-zero center-of-mass momentum q. In the system with the cylindrically symmetric Fermi-surface, it is known that H_c(T) of the d-wave FFLO state exhibits a kink at a low temperature due to a change of the direction of q in contrast to observations in organic superconductors. It is shown that the kink disappears when the Fermi-surface is anisotropic to some extent, since the direction of q is locked in an optimum direction independent of the temperature.Comment: 5 pages, 5 figures, revtex.sty, submitted to J.Phys.Soc.Jp

Superconducting fluctuations at low temperature

The effect of fluctuations on the transport and thermodynamic properties of two-dimensional superconductors in a magnetic field is studied at low temperature. The fluctuation conductivity is calculated in the framework of the perturbation theory with the help of usual diagram technique. It is shown that in the dirty case the Aslamazov-Larkin, Maki-Thomson and Density of States contributions are of the same order. At extremely low temperature, the total fluctuation correction to the normal conductivity is negative in the dirty limit and depends on the external magnetic field logarithmically. In the non-local clean limit, the Aslamazov-Larkin contribution to conductivity is evaluated with the aid of the Helfand-Werthamer theory. The longitudinal and Hall conductivities are found. The fluctuating magnetization is calculated in the one-loop and two-loop approximations.Comment: 12 pages, 4 figures, submitted to Phys. Rev.

Diversity of Raft-Like Domains in Late Endosomes

BACKGROUND: Late endosomes, the last sorting station in the endocytic pathway before lysosomes, are pleiomorphic organelles composed of tubular elements as well as vesicular regions with a characteristic multivesicular appearance, which play a crucial role in intracellular trafficking. Here, we have investigated whether, in addition to these morphologically distinguishable regions, late endosomal membranes are additionally sub-compartmentalized into membrane microdomains. METHODOLOGY/PRINCIPAL FINDINGS: Using sub-organellar fractionation techniques, both with and without detergents, combined with electron microscopy, we found that both the limiting membrane of the organel and the intraluminal vesicles contain raft-type membrane domains. Interestingly, these differentially localized domains vary in protein composition and physico-chemical properties. CONCLUSIONS/SIGNIFICANCE: In addition to the multivesicular organization, we find that late endosomes contain cholesterol rich microdomains both on their limiting membrane and their intraluminal vesicles that differ in composition and properties. Implications of these findings for late endosomal functions are discussed

Metals in high magnetic field: a new universality class of Fermi liquids

Parquet equations, describing the competition between superconducting and density-wave instabilities, are solved for a three-dimensional isotropic metal in a high magnetic field when only the lowest Landau level is filled. In the case of a repulsive interaction between electrons, a phase transition to the density-wave state is found at finite temperature. In the opposite case of attractive interaction, no phase transition is found. With decreasing temperature $T$, the effective vertex of interaction between electrons renormalizes toward a one-dimensional limit in a self-similar way with the characteristic length (transverse to the magnetic field) decreasing as $\ln^{-1/6}(\omega_c/T)$ ($\omega_c$ is a cutoff). Correlation functions have new forms, previously unknown for conventional one-dimensional or three-dimensional Fermi-liquids.Comment: 13 pages + 4 figures (included