Classification of nonproduct states with maximum stabilizer dimension

Nonproduct n-qubit pure states with maximum dimensional stabilizer subgroups of the group of local unitary transformations are precisely the generalized n-qubit Greenberger-Horne-Zeilinger states and their local unitary equivalents, for n greater than or equal to 3 but not equal to 4. We characterize the Lie algebra of the stabilizer subgroup for these states. For n=4, there is an additional maximal stabilizer subalgebra, not local unitary equivalent to the former. We give a canonical form for states with this stabilizer as well.Comment: 6 pages, version 3 has a typographical correction in the displayed equation just after numbered equation (2), and other minor correction

Classification of n-qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits. In this paper we show that any state with minimum orbit dimension must be of this form, and furthermore, such states are classified up to local unitary equivalence by the sets of pairs of qubits entangled in singlets.Comment: 15 pages, latex, revision 2, conclusion added, some proofs shortene

Targeting Mechanisms in Myelinated Axons: Not All Nodes Are Created Equal

A recent Neuron paper by Zhang et al. (2012) reveals how ion channels and adhesion molecules essential for rapid nerve conduction in vertebrates are differentially targeted to nodes of Ranvier. Moreover, distinct mechanisms regulate initial clustering and maintenance of specific nodal components

Sequential primed kinases create a damage-responsive phosphodegron on Eco1.

Sister-chromatid cohesion is established during S phase when Eco1 acetylates cohesin. In budding yeast, Eco1 activity falls after S phase due to Cdk1-dependent phosphorylation, which triggers ubiquitination by SCF(Cdc4). We show here that Eco1 degradation requires the sequential actions of Cdk1 and two additional kinases, Cdc7-Dbf4 and the GSK-3 homolog Mck1. These kinases recognize motifs primed by previous phosphorylation, resulting in an ordered sequence of three phosphorylation events on Eco1. Only the latter two phosphorylation sites are spaced correctly to bind Cdc4, resulting in strict discrimination between phosphates added by Cdk1 and by Cdc7. Inhibition of Cdc7 by the DNA damage response prevents Eco1 destruction, allowing establishment of cohesion after S phase. This elaborate regulatory system, involving three independent kinases and stringent substrate selection by a ubiquitin ligase, enables robust control of cohesion establishment during normal growth and after stress

The approach to criticality in sandpiles

A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model should be equal to the threshold density of the corresponding fixed-energy sandpile. This "density conjecture" has been proved for the underlying graph Z. We show (by simulation or by proof) that the density conjecture is false when the underlying graph is any of Z^2, the complete graph K_n, the Cayley tree, the ladder graph, the bracelet graph, or the flower graph. Driven dissipative sandpiles continue to evolve even after a constant fraction of the sand has been lost at the sink. These results cast doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.Comment: 30 pages, 8 figures, long version of arXiv:0912.320

Minimum orbit dimension for local unitary action on n-qubit pure states

The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.Comment: 19 page

Revisiting remyelination: Towards a consensus on the regeneration of CNS myelin.

The biology of CNS remyelination has attracted considerable interest in recent years because of its translational potential to yield regenerative therapies for the treatment of chronic and progressive demyelinating diseases such as multiple sclerosis (MS). Critical to devising myelin regenerative therapies is a detailed understanding of how remyelination occurs. The accepted dogma, based on animal studies, has been that the myelin sheaths of remyelination are made by oligodendrocytes newly generated from adult oligodendrocyte progenitor cells in a classical regenerative process of progenitor migration, proliferation and differentiation. However, recent human and a growing number of animal studies have revealed a second mode of remyelination in which mature oligodendrocytes surviving within an area of demyelination are able to regenerate new myelin sheaths. This discovery, while opening up new opportunities for therapeutic remyelination, has also raised the question of whether there are fundamental differences in myelin regeneration between humans and some of the species in which experimental remyelination studies are conducted. Here we review how this second mode of remyelination can be integrated into a wider and revised framework for understanding remyelination in which apparent species differences can be reconciled but that also raises important questions for future research.We thank Sarah Neely, University of Edinburgh, for generating the schematic figure. Work in the Franklin lab is supported by UK Multiple Sclerosis Society, the Adelson Medical ResearchFoundation, and a core support grant from the Wellcome and MRC to the Wellcome-MedicalResearch Council Cambridge Stem Cell Institute. , in the Frisen lab by Swedish Research Council, the Swedish Cancer Society, the Swedish Foundation for Strategic Research, Knutoch Alice Wallenbergs Stiftelse and the ERC, and in the Lyons lab by the Wellcome Trust, the UK Multiple Sclerosis Society, the MRC, and Biogen

Emerging biogeochemical views of Earth's ancient microbial worlds

This work was supported by the NASA Astrobiology Institute under Cooperative Agreement No. NNA15BB03A issued through the Science Mission Directorate (TWL), a Natural Environment Research Council Fellowship (NE/H016805/2) (AZ), and National Science Foundation grants (EAR-0951509, OCE-1061476, EAR-1124389, and OCE-1155346) and a Packard Fellowship (DAF).Microbial processes dominate geochemical cycles at and near the Earth’s surface today. Their role was even greater in the past, with microbes being the dominant life form for the first 90% of Earth’s history. Most of their metabolic pathways originated billions of years ago as both causes and effects of environmental changes of the highest order, such as the first accumulation of oxygen in the oceans and atmosphere. Microbial processes leave behind diverse geochemical fingerprints that can remain intact for billions of years. These rock-bound signatures are now steering our understanding of how life coevolved with the environments on early Earth and are guiding our search for life elsewhere in the universe.PostprintPeer reviewe