Building up spacetime with quantum entanglement

In this essay, we argue that the emergence of classically connected spacetimes is intimately related to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum gravity. Disentangling the degrees of freedom associated with two regions of spacetime results in these regions pulling apart and pinching off from each other in a way that can be quantified by standard measures of entanglement.Comment: Gravity Research Foundation essay, 7 pages, LaTeX, 5 figure

Loop Quantum Gravity a la Aharonov-Bohm

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a 3-manifold with a network of defect-lines. A locally-flat connection on this manifold can have non-trivial holonomy around non-contractible loops. This is in fact the mathematical origin of the Aharonov-Bohm effect. I quantize this theory using standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. I argue that the scalar product obtained coincides with the one used in Loop Quantum Gravity. I provide an explicit derivation in the case of a single defect-line, corresponding to a single loop in Loop Quantum Gravity. Moreover, I discuss the relation with spin-networks as used in the context of spin foam models.Comment: 19 pages, 1 figure; v2: corrected typos, section 4 expanded

Network analysis of human glaucomatous optic nerve head astrocytes

<p>Abstract</p> <p>Background</p> <p>Astrocyte activation is a characteristic response to injury in the central nervous system, and can be either neurotoxic or neuroprotective, while the regulation of both roles remains elusive.</p> <p>Methods</p> <p>To decipher the regulatory elements controlling astrocyte-mediated neurotoxicity in glaucoma, we conducted a systems-level functional analysis of gene expression, proteomic and genetic data associated with reactive optic nerve head astrocytes (ONHAs).</p> <p>Results</p> <p>Our reconstruction of the molecular interactions affected by glaucoma revealed multi-domain biological networks controlling activation of ONHAs at the level of intercellular stimuli, intracellular signaling and core effectors. The analysis revealed that synergistic action of the transcription factors AP-1, vitamin D receptor and Nuclear Factor-kappaB in cross-activation of multiple pathways, including inflammatory cytokines, complement, clusterin, ephrins, and multiple metabolic pathways. We found that the products of over two thirds of genes linked to glaucoma by genetic analysis can be functionally interconnected into one epistatic network via experimentally-validated interactions. Finally, we built and analyzed an integrative disease pathology network from a combined set of genes revealed in genetic studies, genes differentially expressed in glaucoma and closely connected genes/proteins in the interactome.</p> <p>Conclusion</p> <p>Our results suggest several key biological network modules that are involved in regulating neurotoxicity of reactive astrocytes in glaucoma, and comprise potential targets for cell-based therapy.</p

Classical Results and Modern Approaches to Nonconservative Stability

Stability of nonconservative systems is nontrivial already on the linear level, especially, if the system depends on multiple parameters. We present an overview of results and methods of stability theory that are specific for nonconservative applications. Special attention is given to the topics of flutter and divergence, reversible- and Hamiltonian-Hopf bifurcation, Krein signature, modes and waves of positive and negative energy, dissipation-induced instabilities, destabilization paradox, influence of structure of forces on stability and stability optimization

Supramolecular assemblies of trinuclear triangular copper(II) secondary building units through hydrogen bonds. Generation of different metal-organic frameworks, valuable catalysts for peroxidative oxidation of alkanes

Formation of the trinuclear triangular copper derivative [Cu3(mu3-OH)(mu-pz)3(EtCOO)2(H2O)].H2O, 1b (Hpz = pyrazole), has been simply achieved by addition of Hpz to a water solution of Cu(EtCOO)2.H2O and leavin g the resulting solution to crystallize at ca. 12 \ub0C. When the reaction and crystallization were carried out at a slightly higher temperature (18-22 \ub0C), the compound [Cu3(mu3-OH)(mu-pz)3(EtCOO)2(H2O)], 1c, formed. Single-crystal X-ray molecular structure determinations show that both compounds have analogous trinuclear triangular structures, but very different supramolecular assemblies, due mainly, but not only, to the crystallization molecule of H2O in 1b. In particular, contrarily to the previously reported, strictly related, [Cu3(mu3-OH)(mu-pz)3(EtCOO)2(EtOH)], 1a, the propionate ions in 1b and 1c do not bridge different triangular units, whereas they are involved in intra- and intermolecular H-bonds, generating complex supramolecular 2-D MOFs. Compounds 1a and 1c act as remarkably active and selective catalysts or catalyst precursors for liquid biphasic (MeCN/H2O) peroxidative oxidation of cyclohexane and cyclopentane to the corresponding alcohols and ketones

Notes on Macdonald polynomials and the geometry of Hilbert schemes

These notes are based on a series of seven lectures given in the combinatorics seminar at U.C. San Diego in February and March, 2001. My lectures at the workshop which is the subject of this proceedings volume covered a portion of the same material in a more abbreviated form

Self-assembly synthesis, structure, topology, and magnetic properties of a mononuclear Fe(iii)-violurate derivative: A combined experimental and theoretical study

A new iron(iii) complex [Fe(H2Vi)3]·py·4H2O (1) {H3Vi = violuric acid, py = pyridine} was self-assembled and characterized. In the crystal structure, adjacent [Fe(H2Vi)3] blocks are H-bonded into a complex 3D network, which was topologically classified as a pcu [alpha-Po primitive cubic] network. Importance of π-stacking interactions was also highlighted and analyzed computationally. Magnetic studies confirmed antiferromagnetic exchange coupling, while ZFCM/FCM experiments indicated an ordering temperature Tc = 50 K. Finally, magnetic hysteresis at 5 K possesses the coercive field of Bc = 69 mT