Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

Geometrical measurements in three-dimensional quantum gravity

A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the distances between points, giving spectra and probabilities which have a geometrical interpretation. The observables are related to the evaluation of relativistic spin networks by a Fourier transform.

The Utilization of Classical Spin Monte Carlo Methods to Simulate the Magnetic Behavior of Extended Three-Dimensional Cubic Networks Incorporating M(II) Ions with an S = 5/2 Ground State Spin

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10−3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH3)4][Mn(N3)] 1, [Mn(CN4)]n 2, and [FeII(bipy)3][MnII2(ox)3] 3, has been carried out. The best fits were those obtained using the following parameters, J = −3.5 cm-1, g = 2.01 (1); J = −8.3 cm-1, g = 1.95 (2); and J = −2.0 cm-1, g = 1.95 (3).

Molecular-Based Magnetism in High-Spin Molecular Clusters and Three-Dimensional Networks Based on Cyanometalate Building Blocks

The field of molecule-based magnets is a relatively new branch of chemistry, which involves the design and study of molecular compounds that exhibit a spontaneous magnetic ordering below a critical temperature, Tc. One major goal involves the design of materials with tuneable Tc's for specific applications in memory storage devices. Molecule-based magnets with high magnetic ordering temperatures have recently been obtained from bimetallic and mixed-valence transition metal μ-cyanide complexes of the Prussian blue family. Since the μ-cyanide linkages permit an interaction between paramagnetic metal ions, cyanometalate building blocks have found useful applications in the field of molecule-based magnets. Our work involves the use of octacyanometalate building blocks for the self-assembly of two new classes of magnetic materials namely, high-spin molecular clusters which exhibit both ferromagnetic intra- and intercluster coupling, and specific extended network topologies which show long-range ferromagnetic ordering.

Research-based spin-offs as agents of knowledge dissemination: evidence from the analysis of innovation networks

The paper addresses the role played by research-based spin-offs (RBSOs) as knowledge dissemination mechanisms, through their position in knowledge networks. For this purpose the paper analyses the formal networks established by the Portuguese RBSOs in the context of publicly funded research, technology and pre-commercial product development projects, and investigates their configuration along two levels. At organisational level, in order to understand whether RBSOs extend their reach beyond the academic sphere; and if they do, whether they relate with similar firms or connect to organisations located downstream in the knowledge value chain, and which is their position in networks involving both research organisations and other firms. At spatial level, in order to understand whether RBSOs extend their reach beyond the region where they are created, thus potentially acting as connectors between diverse regions. The analysis starts from the population of RBSOs created in Portugal until 2007 (387) and identifies those that have established formal technological relationships as part of projects funded by all the programmes launched in the period 1993-2012. As a result, the analysis encompasses 192 collaborative projects and involves 82 spin-offs and 281 partners, of which only 20% are research organisations, the remaining being other firms and a variety of other user organisations. The results, although still preliminary, provide some insights into the knowledge networking behaviour of the RBSOs. As expected, research organisations are a central actor in spin-offs’ networks, being the sole partner for some of them. But half of the RBSOs have moved beyond the academic sphere, being frequently a central element in tripartite technological relationships between research and other organisations and occupying an intermediation position in the network, thus potentially acting as facilitators in knowledge circulation and transformation. Also as expected, RBSOs are predominantly located in the main metropolitan areas and tend to relate with organisations similarly located. But while geographical proximity emerges as important in the choice of partners, in about half of the cases, RBSOs knowledge networks have extended beyond regional boundaries. Given their central position in the network this suggests a role as connectors across regions that will be explored in subsequent research.

Research-based spin-offs as agents of knowledge dissemination: evidence from the analysis of innovation networks

The paper addresses the role played by research-based spin-offs (RBSOs) as knowledge dissemination mechanisms, through their position in knowledge networks. For this purpose the paper analyses the formal networks established by Portuguese RBSOs, in the context of publicly funded research, technology and pre-commercial product development projects, and investigates their configuration across two levels. At organisational level, in order to understand whether RBSOs extend their reach beyond the academic sphere; and if they do, whether they connect to organisations located downstream in the knowledge value chain, and which is their position in networks involving both research organisations and other firms. At spatial level, in order to understand whether RBSOs extend their reach beyond the region where they are created, thus potentially acting as connectors between diverse regions. The analysis starts from the population of RBSOs created in Portugal until 2007 (327 firms) and identifies those that have established formal technological relationships, as part of projects funded by all the relevant programmes launched in the period 1993-2012. As a result, the analysis encompasses 192 collaborative projects and involves 82 spin-offs and 281 partners, of which only 20% are research organisations, the remaining being other firms and a variety of other downstream organisations. The results, although still preliminary, provide some insights into the knowledge networking behaviour of the RBSOs. As expected, research organisations are a central actor in spin-offs’ networks, being the sole partner for some of them. But half of the RBSOs have moved beyond the academic sphere, being frequently a central element in tripartite technological relationships between research and other organisations, and occupying an intermediation position in the network, thus potentially acting as facilitators in knowledge circulation and transformation. Also as expected, RBSOs are predominantly located in the main metropolitan areas and tend to relate with organisations similarly located. But while geographical proximity emerges as important in the choice of partners, in about half of the cases, RBSOs knowledge networks have extended beyond regional boundaries. Given their central position in the network, this suggests a role as connectors across regions that will be explored in subsequent research.

Loops, Chains, Sheets, and Networks from Variable Coordination of Cu(hfac)(2) with a Flexibly Hinged Aminoxyl Radical Ligand

One pair of reactants, Cu(hfac)(2) = M and the hinge-flexible radical ligand 5-(3-N-tert-butyl-N-aminoxylphenyl)pyrimidine (3PPN = L), yields a diverse set of five coordination complexes: a cyclic loop M(2)L(1) dimer; a 1:1 cocrystal between an M(2)L(2) loop and an ML(2) fragment; a ID chain of M(2)L(2) loops linked by M; two 2D M(3)L(2) networks of (M-L)(n) chains crosslinked by M with different repeat length pitches; a 3D M(3)L(2) network of M(2)L(2) loops cross-linking (M-L)(n)-type chains with connectivity different from those in the 2D networks. Most of the higher dimensional complexes exhibit reversible, temperature-dependent spin-state conversion of high-temperature paramagnetic states to lower magnetic moment states having antiferromagnetic exchange within Cu-ON bonds upon cooling, with accompanying bond contraction. The 3D complex also exhibited antiferromagnetic exchange between Cu(II) ions linked in chains through pyrimidine rings.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

A Homonuclear Rotational Echo Double-Resonance Method for Measuring Site-Resolved Distance Distributions in I=1/2 Spin Pairs, Clusters, and Multispin Systems

Deutsche Forschungsgemeinschaft [SFB 858]

Functional connectivity in BOLD and CBF data: similarity and reliability of resting brain networks

Resting-state functional connectivity (FC) fMRI (rs-fcMRI) offers an appealing approach to mapping the brain's intrinsic functional organization. Blood oxygen level dependent (BOLD) and arterial spin labeling (ASL) are the two main rs-fcMRI approaches to assess alterations in brain networks associated with individual differences, behavior and psychopathology. While the BOLD signal is stronger with a higher temporal resolution, ASL provides quantitative, direct measures of the physiology and metabolism of specific networks. This study systematically investigated the similarity and reliability of resting brain networks (RBNs) in BOLD and ASL. A 2×2×2 factorial design was employed where each subject underwent repeated BOLD and ASL rs-fcMRI scans on two occasions on two MRI scanners respectively. Both independent and joint FC analyses revealed common RBNs in ASL and BOLD rs-fcMRI with a moderate to high level of spatial overlap, verified by Dice Similarity Coefficients. Test-retest analyses indicated more reliable spatial network patterns in BOLD (average modal Intraclass Correlation Coefficients: 0.905±0.033 between-sessions; 0.885±0.052 between-scanners) than ASL (0.545±0.048; 0.575±0.059). Nevertheless, ASL provided highly reproducible (0.955±0.021; 0.970±0.011) network-specific CBF measurements. Moreover, we observed positive correlations between regional CBF and FC in core areas of all RBNs indicating a relationship between network connectivity and its baseline metabolism. Taken together, the combination of ASL and BOLD rs-fcMRI provides a powerful tool for characterizing the spatiotemporal and quantitative properties of RBNs. These findings pave the way for future BOLD and ASL rs-fcMRI studies in clinical populations that are carried out across time and scanners.

Interhemispheric cerebral blood flow balance during recovery of motor hand function after ischemic stroke - a longitudinal MRI study using arterial spin labeling perfusion

BACKGROUND Unilateral ischemic stroke disrupts the well balanced interactions within bilateral cortical networks. Restitution of interhemispheric balance is thought to contribute to post-stroke recovery. Longitudinal measurements of cerebral blood flow (CBF) changes might act as surrogate marker for this process. OBJECTIVE To quantify longitudinal CBF changes using arterial spin labeling MRI (ASL) and interhemispheric balance within the cortical sensorimotor network and to assess their relationship with motor hand function recovery. METHODS Longitudinal CBF data were acquired in 23 patients at 3 and 9 months after cortical sensorimotor stroke and in 20 healthy controls using pulsed ASL. Recovery of grip force and manual dexterity was assessed with tasks requiring power and precision grips. Voxel-based analysis was performed to identify areas of significant CBF change. Region-of-interest analyses were used to quantify the interhemispheric balance across nodes of the cortical sensorimotor network. RESULTS Dexterity was more affected, and recovered at a slower pace than grip force. In patients with successful recovery of dexterous hand function, CBF decreased over time in the contralesional supplementary motor area, paralimbic anterior cingulate cortex and superior precuneus, and interhemispheric balance returned to healthy control levels. In contrast, patients with poor recovery presented with sustained hypoperfusion in the sensorimotor cortices encompassing the ischemic tissue, and CBF remained lateralized to the contralesional hemisphere. CONCLUSIONS Sustained perfusion imbalance within the cortical sensorimotor network, as measured with task-unrelated ASL, is associated with poor recovery of dexterous hand function after stroke. CBF at rest might be used to monitor recovery and gain prognostic information.

Chiral, Three-Dimensional Supramolecular Compounds: Homo- and Bimetallic Oxalate- and 1,2-Dithiooxalate-Bridged Networks. A Structural and Photophysical Study.

In analogy to the [M(II)(bpy)(3)](2+) cations, where M(II) is a divalent transition-metal and bpy is 2,2'-bipyridine, the tris-chelated [M(III)(bpy)(3)](3+) cations, where M(III) is Cr(III) or Co(III), induce the crystallization of chiral, anionic three-dimensional (3D) coordination polymers of oxalate-bridged (&mgr;-ox) metal complexes with stoichiometries [M(II)(2)(ox)(3)](n)()(2)(n)()(-) or [M(I)M(III)(ox)(3)](n)()(2)(n)()(-). The tripositive charge is partially compensated by inclusion of additional complex anions like ClO(4)(-), BF(4)(-), or PF(6)(-) which are encapsulated in cubic shaped cavities formed by the bipyridine ligands of the cations. Thus, an elaborate structure of cationic and anionic species within a polymeric anionic network is realized. The compounds isolated and structurally characterized include [Cr(III)(bpy)(3)][ClO(4)] [NaCr(III)(ox)(3)] (1), [Cr(III)(bpy)(3)][ClO(4)][Mn(II)(2)(ox)(3)] (2), [Cr(III)(bpy)(3)][BF(4)] [Mn(II)(2)(ox)(3)] (3), [Co(III)(bpy)(3)][PF(6)][NaCr(III)(ox)(3)] (4). Crystal data: 1, cubic, P2(1)3, a = 15.523(4) Å, Z = 4; 2, cubic, P4(1)32, a = 15.564(3) Å, Z = 4; 3, cubic, P4(1)32, a = 15.553(3) Å, Z = 4; 4, cubic, P2(1)3, a = 15.515(3) Å, Z = 4. Furthermore, it seemed likely that 1,2-dithiooxalate (dto) could act as an alternative to the oxalate bridging ligand, and as a result the compound [Ni(II)(phen)(3)][NaCo(III)(dto)(3)].C(3)H(6)O (5) has successfully been isolated and structurally characterized. Crystal data: 5, orthorhombic, P2(1)2(1)2(1), a = 16.238(4) Å, b = 16.225(4) Å, c = 18.371(5) Å, Z = 4. In addition, the photophysical properties of compound 1 have been investigated in detail. In single crystal absorption spectra of [Cr(III)(bpy)(3)][ClO(4)][NaCr(III)(ox)(3)] (1), the spin-flip transitions of both the [Cr(bpy)(3)](3+) and the [Cr(ox)(3)](3)(-) chromophores are observed and can be clearly distinguished. Irradiating into the spin-allowed (4)A(2) --> (4)T(2) absorption band of [Cr(ox)(3)](3)(-) results in intense luminescence from the (2)E state of [Cr(bpy)(3)](3+) as a result of rapid energy transfer processes.