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

On Myelinated Axon Plasticity and Neuronal Circuit Formation and Function

Studies of activity-driven nervous system plasticity have primarily focused on the gray matter. However, MRI-based imaging studies have shown that white matter, primarily composed of myelinated axons, can also be dynamically regulated by activity of the healthy brain. Myelination in the CNS is an ongoing process that starts around birth and continues throughout life. Myelin in the CNS is generated by oligodendrocytes and recent evidence has shown that many aspects of oligodendrocyte development and myelination can be modulated by extrinsic signals including neuronal activity. Because modulation of myelin can, in turn, affect several aspects of conduction, the concept has emerged that activity-regulated myelination represents an important form of nervous system plasticity. Here we review our increasing understanding of how neuronal activity regulates oligodendrocytes and myelinated axons in vivo, with a focus on the timing of relevant processes. We highlight the observations that neuronal activity can rapidly tune axonal diameter, promote re-entry of oligodendrocyte progenitor cells into the cell cycle, or drive their direct differentiation into oligodendrocytes. We suggest that activity-regulated myelin formation and remodeling that significantly change axonal conduction properties are most likely to occur over timescales of days to weeks. Finally, we propose that precise fine-tuning of conduction along already-myelinated axons may also be mediated by alterations to the axon itself. We conclude that future studies need to analyze activity-driven adaptations to both axons and their myelin sheaths to fully understand how myelinated axon plasticity contributes to neuronal circuit formation and function.</p

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

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

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

Are There Local Analogs of Lyman Break Galaxies?

To make direct comparisons in the rest-far-ultraviolet between LBGs at z~3 and more local star-forming galaxies, we use HST/STIS to image a set of 12 nearby (z<0.05) HII galaxies in the FUV and a set of 14 luminous compact blue galaxies (LCBGs) at moderate redshift (z~0.5) in the NUV, corresponding to the rest-FUV. We then subject both sets of galaxy images and those of LBGs at z~3 to the same morphological and structural analysis. We find many qualitative and quantitative similarities between the rest-FUV characteristics of distant LBGs and of the more nearby starburst samples, including general morphologies, sizes, asymmetries, and concentrations. Along with some kinematic similarities, this implies that nearby HII galaxies and LCBGs may be reasonable local analogs of distant Lyman break galaxies.Comment: 4 pages, 4 figures. To appear in "Starbursts: from 30 Doradus to Lyman Break Galaxies" 2005, eds. R. de Grijs and R. M. Gonzalez Delgado (Kluwer

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

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

Light sheet microscopy with acoustic sample confinement

Contactless sample confinement would enable a whole host of new studies in developmental biology and neuroscience, in particular, when combined with long-term, wide-field optical imaging. To achieve this goal, we demonstrate a contactless acoustic gradient force trap for sample confinement in light sheet microscopy. Our approach allows the integration of real-time environmentally controlled experiments with wide-field low photo-toxic imaging, which we demonstrate on a variety of marine animal embryos and larvae. To illustrate the key advantages of our approach, we provide quantitative data for the dynamic response of the heartbeat of zebrafish larvae to verapamil and norepinephrine, which are known to affect cardiovascular function. Optical flow analysis allows us to explore the cardiac cycle of the zebrafish and determine the changes in contractile volume within the heart. Overcoming the restrictions of sample immobilisation and mounting can open up a broad range of studies, with real-time drug-based assays and biomechanical analyses.</p

Major features and forcing of high‐latitude northern hemisphere atmospheric circulation using a 110,000‐year‐long glaciochemical series

The Greenland Ice Sheet Project 2 glaciochemical series (sodium, potassium, ammonium, calcium, magnesium, sulfate, nitrate, and chloride) provides a unique view of the chemistry of the atmosphere and the history of atmospheric circulation over both the high latitudes and mid‐low latitudes of the northern hemisphere. Interpretation of this record reveals a diverse array of environmental signatures that include the documentation of anthropogenically derived pollutants, volcanic and biomass burning events, storminess over marine surfaces, continental aridity and biogenic source strength plus information related to the controls on both high‐ and low‐frequency climate events of the last 110,000 years. Climate forcings investigated include changes in insolation of the order of the major orbital cycles that control the long‐term behavior of atmospheric circulation patterns through changes in ice volume (sea level), events such as the Heinrich events (massive discharges of icebergs first identified in the marine record) that are found to operate on a 6100‐year cycle due largely to the lagged response of ice sheets to changes in insolation and consequent glacier dynamics, and rapid climate change events (massive reorganizations of atmospheric circulation) that are demonstrated to operate on 1450‐year cycles. Changes in insolation and associated positive feedbacks related to ice sheets may assist in explaining favorable time periods and controls on the amplitude of massive rapid climate change events. Explanation for the exact timing and global synchroneity of these events is, however, more complicated. Preliminary evidence points to possible solar variability‐climate associations for these events and perhaps others that are embedded in our ice‐core‐derived atmospheric circulation records