Syzygies, Betti numbers and regularity of cover ideals of certain multipartite graphs

Let $G$ be a finite simple graph on $n$ vertices. Let $J_G \subset K[x_1, \ldots, x_n]$ be the cover ideal of $G$. In this article, we obtain syzygies, Betti numbers and Castelnuovo-Mumford regularity of $J_G^s$ for all $s \geq 1$ for certain classes of graphs $G$.Comment: Title and other minor change

Electronic inhomogeneities in the superconducting phase of CaFe1.96Ni0.04As2 single crystals

Superconductivity in Iron-Arsenic based pnictides emerges in close proximity to an antiferromagnetic (AFM)ordered parent state and the AFM phase overlaps with superconducting (SC) phase in some pnictides for certain range of doping. CaFe2-xNixAs2 belongs to this category, where both the phases overlap. Here we use scanning tunneling microscopy and spectroscopy to investigate the local electronic properties of uderdoped CaFe1.96Ni0.04As2 single crystals in the vicinity of the boundary of the two phases. Both resistivity and magnetic measurements show that a tiny portion (~ 1.2 %) of this compound becomes superconductor below the SC onset temperature TC ~ 15 K. Topographic images show reasonably flat surface with signatures of atomic resolution. High temperature spectra are spatially homogeneous and show signatures of spin density wave (SDW) gap with a finite density of states near the Fermi energy. Below TC, spectra show significant spatial inhomogeneity with a SDW gap everywhere but at some locations we also see an asymmetric or symmetric depression in ~ +/- 5 meV energy range together with the SDW gap. Inhomogeneity reduces significantly as the temperature goes above TC and disappears completely far above TC. These observations are discussed in terms of an inhomogeneous electronic phase that may exist due to the vicinity of this composition to the SC dome boundary on the underdoped side of the phase diagram

First Principles LCGO Calculation of the Magneto-optical Properties of Nickel and Iron

We report a first principles, self-consistent, all electron, linear combination of Gaussian orbitals (LCGO) calculation of a comprehensive collection of magneto-optical properties of nickel and iron based on density functional theory. Among the many magneto-optical effects, we have studied the equatorial Kerr effect for absorption in the optical as well as soft X-ray region, where it is called X-ray magnetic linear dichroism (X-MLD). In the optical region the effect is of the order of 2\% while in the X-ray region it is of the order of 1\% for the incident angles considered. In addition, the polar Kerr effect, X-ray magnetic circular dichroism (X-MCD) and total X-ray absorption at the L$_{2,3}$ edges, soft X-ray Faraday effect at the L$_{2,3}$ edges have also been calculated. Our results are in good agreement with experiments and other first principles methods that have been used to calculate some of these properties.Comment: 22 pages RevTex. 8 figures submitted separately as a uuencoded, compressed tar fil

Anomalous local magnetic field distribution and strong pinning in CaFe1.94Co0.06As2 single crystals

Magneto-optical imaging of a single crystal of CaFe1.94Co0.06As2, shows anomalous remnant magnetization within Meissner like regions of the superconductor. The unconventional shape of the local magnetization hysteresis loop suggests admixture of superconducting and magnetic fractions governing the response. Near the superconducting transition temperature, local magnetic field exceeds the applied field resulting in a diamagnetic to positive magnetization transformation. The observed anomalies in the local magnetic field distribution are accompanied with enhanced bulk pinning in the CaFe1.94Co0.06As2 single crystals. We propose our results suggest a coexistence of superconductivity and magnetic correlations.Comment: 6 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1201.369

FLOWERING LOCUS C -dependent and -independent regulation of the circadian clock by the autonomous and vernalization pathways

Background The circadian system drives pervasive biological rhythms in plants. Circadian clocks integrate endogenous timing information with environmental signals, in order to match rhythmic outputs to the local day/night cycle. Multiple signaling pathways affect the circadian system, in ways that are likely to be adaptively significant. Our previous studies of natural genetic variation in Arabidopsis thaliana accessions implicated FLOWERING LOCUS C (FLC) as a circadian-clock regulator. The MADS-box transcription factor FLC is best known as a regulator of flowering time. Its activity is regulated by many regulatory genes in the "autonomous" and vernalization-dependent flowering pathways. We tested whether these same pathways affect the circadian system. Results Genes in the autonomous flowering pathway, including FLC, were found to regulate circadian period in Arabidopsis. The mechanisms involved are similar, but not identical, to the control of flowering time. By mutant analyses, we demonstrate a graded effect of FLC expression upon circadian period. Related MADS-box genes had less effect on clock function. We also reveal an unexpected vernalization-dependent alteration of periodicity. Conclusion This study has aided in the understanding of FLC's role in the clock, as it reveals that the network affecting circadian timing is partially overlapping with the floral-regulatory network. We also show a link between vernalization and circadian period. This finding may be of ecological relevance for developmental programing in other plant species