Linear recurring sequence subgroups in finite fields

AbstractGiven a finite field F and a linear recurrence relation over F it is possible to find, in a fairly “obvious” way, a finite extension L of F and a subgroup M of the multiplicative group of L such that the elements of M may be written, without repetition, so as to form a cyclically closed sequence which obeys the recurrence. Here we investigate this phenomenon for second-order recurrences; the situation in which F has prime order and the characteristic polynomial of the relation is irreducible over F is described

Global Gene Expression Profiling of Individual Human Oocytes and Embryos Demonstrates Heterogeneity in Early Development

Early development in humans is characterised by low and variable embryonic viability, reflected in low fecundity and high rates of miscarriage, relative to other mammals. Data from assisted reproduction programmes provides additional evidence that this is largely mediated at the level of embryonic competence and is highly heterogeneous among embryos. Understanding the basis of this heterogeneity has important implications in a number of areas including: the regulation of early human development, disorders of pregnancy, assisted reproduction programmes, the long term health of children which may be programmed in early development, and the molecular basis of pluripotency in human stem cell populations. We have therefore investigated global gene expression profiles using polyAPCR amplification and microarray technology applied to individual human oocytes and 4-cell and blastocyst stage embryos. In order to explore the basis of any variability in detail, each developmental stage is replicated in triplicate. Our data show that although transcript profiles are highly stage-specific, within each stage they are relatively variable. We describe expression of a number of gene families and pathways including apoptosis, cell cycle and amino acid metabolism, which are variably expressed and may be reflective of embryonic developmental competence. Overall, our data suggest that heterogeneity in human embryo developmental competence is reflected in global transcript profiles, and that the vast majority of existing human embryo gene expression data based on pooled oocytes and embryos need to be reinterpreted

Assessment of the U and Co magnetic moments in UCoGe by X-ray magnetic circular dichroism

The ferromagnetic superconductor UCoGe has been investigated by high field X-ray magnetic circular dichroism (XMCD) at the U-M$_{4,5}$ and Co/Ge-K edges. The analysis of the branching ratio and XMCD at the U-M$_{4,5}$ edges reveals that the U-5$f$ electrons count is close to 3. The orbital ($\sim0.70\,\mu_B$) and spin ($\sim-0.30\,\mu_B$) moments of U at 2.1K and 17T (H//c) have been determined. Their ratio ($\sim-2.3$) suggests a significant delocalization of the 5$f$ electron states. The similar field dependences of the local U/Co and the macroscopic magnetization indicate that the Co moment is induced by the U moment. The XMCD at the Co/Ge-K edges reveal the presence of small Co-4$p$ and Ge-4$p$ orbital moments parallel to the macroscopic magnetization. In addition, the Co-3$d$ moment is estimated to be at most of the order of 0.1$\mu_B$ at 17T. Our results rule out the possibility of an unusual polarisability of the U and Co moments as well as their antiparallel coupling. We conclude that the magnetism which mediates the superconductivity in UCoGe is driven by U.Comment: 4 figures + supplementary materia

Global gene expression profiling of individual human oocytes and embryos demonstrates heterogeneity in early development

Early development in humans is characterised by low and variable embryonic viability, reflected in low fecundity and high rates of miscarriage, relative to other mammals. Data from assisted reproduction programmes provides additional evidence that this is largely mediated at the level of embryonic competence and is highly heterogeneous among embryos. Understanding the basis of this heterogeneity has important implications in a number of areas including: the regulation of early human development, disorders of pregnancy, assisted reproduction programmes, the long term health of children which may be programmed in early development, and the molecular basis of pluripotency in human stem cell populations. We have therefore investigated global gene expression profiles using polyAPCR amplification and microarray technology applied to individual human oocytes and 4-cell and blastocyst stage embryos. In order to explore the basis of any variability in detail, each developmental stage is replicated in triplicate. Our data show that although transcript profiles are highly stage-specific, within each stage they are relatively variable. We describe expression of a number of gene families and pathways including apoptosis, cell cycle and amino acid metabolism, which are variably expressed and may be reflective of embryonic developmental competence. Overall, our data suggest that heterogeneity in human embryo developmental competence is reflected in global transcript profiles, and that the vast majority of existing human embryo gene expression data based on pooled oocytes and embryos need to be reinterpreted

Thermal conductivity through the quantum critical point in YbRh2Si2 at very low temperature

The thermal conductivity of YbRh2Si2 has been measured down to very low temperatures under field in the basal plane. An additional channel for heat transport appears below 30 mK, both in the antiferromagnetic and paramagnetic states, respectively below and above the critical field suppressing the magnetic order. This excludes antiferromagnetic magnons as the origin of this additional contribution to thermal conductivity. Moreover, this low temperature contribution prevails a definite conclusion on the validity or violation of the Wiedemann-Franz law at the field-induced quantum critical point. At high temperature in the paramagnetic state, the thermal conductivity is sensitive to ferromagnetic fluctuations, previously observed by NMR or neutron scattering and required for the occurrence of the sharp electronic spin resonance fracture.Comment: 11 pages + Supplementary Material